laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=4, ny=4 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.3333333333333333)=0.0 i=2, Ua(0.6666666666666666)=0.0 i=3, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.3333333333333333)=0.3271946967961522 ii=2, Ua(0.6666666666666666)=0.618369803069737 ii=3, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=3 xx[1]=0.1127016653792583, xx[2]=0.5, wx[1]=0.27777777777777635, wx[2]=0.4444444444444444 calling gauleg ymin=0.0, ymax=1.0, npy=3 yy[1]=0.1127016653792583, yy[2]=0.5, wy[1]=0.27777777777777635, wy[2]=0.4444444444444444 galk(xx[2],yy[2])=-1.6018066406249971 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=0.03369513790223699, rmserr=0.02051189786487502, avgerr=0.01788794923282544 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.3271946967961522, Ua=0.3271946967961522, err=0.0 ug[0,2]=0.618369803069737, Ua=0.618369803069737, err=0.0 ug[0,3]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=0.0, Ua=0.0, err=0.0 ug[1,1]=0.456590518524976, Ua=0.45663698427098576, err=-4.646574600974951E-5 ug[1,2]=0.8628090675190013, Ua=0.8630045804621632, err=-1.9551294316189072E-4 ug[1,3]=1.1743673617473285, Ua=1.1743673617473285, err=0.0 ug[2,0]=0.0, Ua=0.0, err=0.0 ug[2,1]=0.6371959388771039, Ua=0.6372882490024289, err=-9.231012532495697E-5 ug[2,2]=1.204031545701788, Ua=1.2044199153992028, err=-3.883696974147366E-4 ug[2,3]=1.638961681670142, Ua=1.638961681670142, err=0.0 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=0.8894073986691476, Ua=0.8894073986691476, err=0.0 ug[3,2]=1.6809033989522646, Ua=1.6809033989522646, err=0.0 ug[3,3]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=4, ny=4, npx=3, npy=3 maxerr=3.883696974147366E-4, avgerr=4.516615699445836E-5 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=4, ny=4 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.3333333333333333)=0.0 i=2, Ua(0.6666666666666666)=0.0 i=3, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.3333333333333333)=0.3271946967961522 ii=2, Ua(0.6666666666666666)=0.618369803069737 ii=3, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=4 xx[1]=0.06943184420297371, xx[2]=0.33000947820757187, wx[1]=0.1739274225687238, wx[2]=0.3260725774312732 calling gauleg ymin=0.0, ymax=1.0, npy=4 yy[1]=0.06943184420297371, yy[2]=0.33000947820757187, wy[1]=0.1739274225687238, wy[2]=0.3260725774312732 galk(xx[2],yy[2])=-37.07665038405839 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=0.02865596651435176, rmserr=0.019262403091239902, avgerr=0.017887949232830325 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.3271946967961522, Ua=0.3271946967961522, err=0.0 ug[0,2]=0.618369803069737, Ua=0.618369803069737, err=0.0 ug[0,3]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=1.3877787807814457E-17, Ua=0.0, err=1.3877787807814457E-17 ug[1,1]=0.4565194544367737, Ua=0.45663698427098576, err=-1.1752983421203789E-4 ug[1,2]=0.8628112733423158, Ua=0.8630045804621632, err=-1.933071198474412E-4 ug[1,3]=1.1743673617473285, Ua=1.1743673617473285, err=0.0 ug[2,0]=2.3327220696093617E-17, Ua=0.0, err=2.3327220696093617E-17 ug[2,1]=0.6371386027379529, Ua=0.6372882490024289, err=-1.4964626447599993E-4 ug[2,2]=1.2041577401058257, Ua=1.2044199153992028, err=-2.621752933771315E-4 ug[2,3]=1.638961681670142, Ua=1.638961681670142, err=0.0 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=0.8894073986691476, Ua=0.8894073986691476, err=0.0 ug[3,2]=1.6809033989522646, Ua=1.6809033989522646, err=0.0 ug[3,3]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=4, ny=4, npx=4, npy=4 maxerr=2.621752933771315E-4, avgerr=4.5166156994540483E-5 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=4, ny=4 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.3333333333333333)=0.0 i=2, Ua(0.6666666666666666)=0.0 i=3, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.3333333333333333)=0.3271946967961522 ii=2, Ua(0.6666666666666666)=0.618369803069737 ii=3, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=6 xx[1]=0.033765242898423975, xx[2]=0.1693953067668677, wx[1]=0.08566224618958117, wx[2]=0.1803807865240693 calling gauleg ymin=0.0, ymax=1.0, npy=6 yy[1]=0.033765242898423975, yy[2]=0.1693953067668677, wy[1]=0.08566224618958117, wy[2]=0.1803807865240693 galk(xx[2],yy[2])=-52.717097366724644 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=0.028655966514341102, rmserr=0.01926240309122914, avgerr=0.01788794923282011 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.3271946967961522, Ua=0.3271946967961522, err=0.0 ug[0,2]=0.6183698030697369, Ua=0.618369803069737, err=-1.1102230246251565E-16 ug[0,3]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=3.8316517662831575E-16, Ua=0.0, err=3.8316517662831575E-16 ug[1,1]=0.4565194544367743, Ua=0.45663698427098576, err=-1.1752983421148278E-4 ug[1,2]=0.8628112733423166, Ua=0.8630045804621632, err=-1.9330711984666404E-4 ug[1,3]=1.1743673617473285, Ua=1.1743673617473285, err=0.0 ug[2,0]=-7.658095303682502E-17, Ua=0.0, err=-7.658095303682502E-17 ug[2,1]=0.6371386027379533, Ua=0.6372882490024289, err=-1.4964626447555585E-4 ug[2,2]=1.2041577401058263, Ua=1.2044199153992028, err=-2.621752933764654E-4 ug[2,3]=1.638961681670142, Ua=1.638961681670142, err=0.0 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=0.8894073986691476, Ua=0.8894073986691476, err=0.0 ug[3,2]=1.6809033989522646, Ua=1.6809033989522646, err=0.0 ug[3,3]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=4, ny=4, npx=6, npy=6 maxerr=2.621752933764654E-4, avgerr=4.5166156994421174E-5 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=6, ny=6 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.2)=0.0 i=2, Ua(0.4)=0.0 i=3, Ua(0.6000000000000001)=0.0 i=4, Ua(0.8)=0.0 i=5, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.2)=0.19866933079506122 ii=2, Ua(0.4)=0.3894183423086505 ii=3, Ua(0.6000000000000001)=0.5646424733950355 ii=4, Ua(0.8)=0.7173560908995228 ii=5, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=4 xx[1]=0.06943184420297371, xx[2]=0.33000947820757187, wx[1]=0.1739274225687238, wx[2]=0.3260725774312732 calling gauleg ymin=0.0, ymax=1.0, npy=4 yy[1]=0.06943184420297371, yy[2]=0.33000947820757187, wy[1]=0.1739274225687238, wy[2]=0.3260725774312732 galk(xx[2],yy[2])=0.9529561719947807 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=4.278713626391095E-4, rmserr=2.4175780468213177E-4, avgerr=1.9000319653900144E-4 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=-1.3082876709315805E-15, Ua=0.0, err=-1.3082876709315805E-15 ug[0,1]=0.19866933079506122, Ua=0.19866933079506122, err=0.0 ug[0,2]=0.38941834230865174, Ua=0.3894183423086505, err=1.2212453270876722E-15 ug[0,3]=0.5646424733950354, Ua=0.5646424733950355, err=-1.1102230246251565E-16 ug[0,4]=0.7173560908995228, Ua=0.7173560908995228, err=0.0 ug[0,5]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=-2.3406952893173123E-15, Ua=0.0, err=-2.3406952893173123E-15 ug[1,1]=0.2426556956308315, Ua=0.24265526859492295, err=4.2703590855119877E-7 ug[1,2]=0.4756343984745161, Ua=0.4756366373739469, err=-2.2388994307953602E-6 ug[1,3]=0.6896531629353059, Ua=0.6896558743790767, err=-2.7114437708419814E-6 ug[1,4]=0.8761798207198545, Ua=0.8761807080076747, err=-8.872878202170753E-7 ug[1,5]=1.027774981756119, Ua=1.0277749817561193, err=-2.220446049250313E-16 ug[2,0]=0.0, Ua=0.0, err=0.0 ug[2,1]=0.2963815778837627, Ua=0.29637981434393573, err=1.763539826948879E-6 ug[2,2]=0.580943765266738, Ua=0.5809439007705672, err=-1.3550382926830196E-7 ug[2,3]=0.8423481045504718, Ua=0.8423475871479679, err=5.174025039522689E-7 ug[2,4]=1.0701731826596073, Ua=1.0701695334073043, err=3.6492523030062785E-6 ug[2,5]=1.2553271974849423, Ua=1.2553271974849423, err=0.0 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=0.36200112824473585, Ua=0.3619991227026822, err=2.0055420536513324E-6 ug[3,2]=0.7095659950238513, Ua=0.7095664827374989, err=-4.877136475789356E-7 ug[3,3]=1.0288458317555456, Ua=1.028845666272092, err=1.654834536068961E-7 ug[3,4]=1.3071119682007044, Ua=1.3071080198026634, err=3.948398040964918E-6 ug[3,5]=1.5332601014015845, Ua=1.5332601014015848, err=-2.220446049250313E-16 ug[4,0]=0.0, Ua=0.0, err=0.0 ug[4,1]=0.44214790069776555, Ua=0.4421467269206178, err=1.1737771477560166E-6 ug[4,2]=0.8666631910729807, Ua=0.8666664591135917, err=-3.268040611015266E-6 ug[4,3]=1.2566311370949836, Ua=1.256634934505871, err=-3.7974108872962375E-6 ug[4,4]=1.59650520421945, Ua=1.5965053406002512, err=-1.3638080109679152E-7 ug[4,5]=1.8727281168288372, Ua=1.8727281168288372, err=0.0 ug[5,0]=0.0, Ua=0.0, err=0.0 ug[5,1]=0.5400392317723339, Ua=0.5400392317723339, err=0.0 ug[5,2]=1.0585488035662491, Ua=1.0585488035662491, err=0.0 ug[5,3]=1.534857375005895, Ua=1.534857375005895, err=0.0 ug[5,4]=1.9499760264265882, Ua=1.9499760264265882, err=0.0 ug[5,5]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=6, ny=6, npx=4, npy=4 maxerr=3.948398040964918E-6, avgerr=7.586975567214744E-7 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=6, ny=6 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.2)=0.0 i=2, Ua(0.4)=0.0 i=3, Ua(0.6000000000000001)=0.0 i=4, Ua(0.8)=0.0 i=5, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.2)=0.19866933079506122 ii=2, Ua(0.4)=0.3894183423086505 ii=3, Ua(0.6000000000000001)=0.5646424733950355 ii=4, Ua(0.8)=0.7173560908995228 ii=5, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=6 xx[1]=0.033765242898423975, xx[2]=0.1693953067668677, wx[1]=0.08566224618958117, wx[2]=0.1803807865240693 calling gauleg ymin=0.0, ymax=1.0, npy=6 yy[1]=0.033765242898423975, yy[2]=0.1693953067668677, wy[1]=0.08566224618958117, wy[2]=0.1803807865240693 galk(xx[2],yy[2])=-174.7394764322955 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=2.4116836741416847E-4, rmserr=1.3519566317755628E-4, avgerr=1.0591916954721947E-4 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.1986693307950609, Ua=0.19866933079506122, err=-3.0531133177191805E-16 ug[0,2]=0.3894183423086506, Ua=0.3894183423086505, err=5.551115123125783E-17 ug[0,3]=0.5646424733950355, Ua=0.5646424733950355, err=0.0 ug[0,4]=0.7173560908995229, Ua=0.7173560908995228, err=1.1102230246251565E-16 ug[0,5]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=1.2787485045873995E-15, Ua=0.0, err=1.2787485045873995E-15 ug[1,1]=0.2426554143667268, Ua=0.24265526859492295, err=1.4577180385000332E-7 ug[1,2]=0.4756358710370552, Ua=0.4756366373739469, err=-7.663368917221192E-7 ug[1,3]=0.6896548184592654, Ua=0.6896558743790767, err=-1.0559198113657686E-6 ug[1,4]=0.8761803471402881, Ua=0.8761807080076747, err=-3.6086738652851835E-7 ug[1,5]=1.0277749817561193, Ua=1.0277749817561193, err=0.0 ug[2,0]=3.8487679351026876E-16, Ua=0.0, err=3.8487679351026876E-16 ug[2,1]=0.2963805255416867, Ua=0.29637981434393573, err=7.111977509688394E-7 ug[2,2]=0.5809438892527203, Ua=0.5809439007705672, err=-1.1517846898456696E-8 ug[2,3]=0.8423476076344631, Ua=0.8423475871479679, err=2.0486495277971528E-8 ug[2,4]=1.0701706374405102, Ua=1.0701695334073043, err=1.104033205967525E-6 ug[2,5]=1.2553271974849423, Ua=1.2553271974849423, err=0.0 ug[3,0]=1.4057469159225372E-33, Ua=0.0, err=1.4057469159225372E-33 ug[3,1]=0.361999968425093, Ua=0.3619991227026822, err=8.457224108249228E-7 ug[3,2]=0.7095664541719987, Ua=0.7095664827374989, err=-2.856550018748294E-8 ug[3,3]=1.0288456699859918, Ua=1.028845666272092, err=3.71389985431847E-9 ug[3,4]=1.307109331625912, Ua=1.3071080198026634, err=1.3118232484732317E-6 ug[3,5]=1.5332601014015848, Ua=1.5332601014015848, err=0.0 ug[4,0]=-5.06473702938077E-17, Ua=0.0, err=-5.06473702938077E-17 ug[4,1]=0.44214715220410616, Ua=0.4421467269206178, err=4.252834883700096E-7 ug[4,2]=0.8666654919181989, Ua=0.8666664591135917, err=-9.671953928869215E-7 ug[4,3]=1.256633602832373, Ua=1.256634934505871, err=-1.3316734979174072E-6 ug[4,4]=1.5965052591861253, Ua=1.5965053406002512, err=-8.141412588535957E-8 ug[4,5]=1.8727281168288372, Ua=1.8727281168288372, err=0.0 ug[5,0]=0.0, Ua=0.0, err=0.0 ug[5,1]=0.5400392317723339, Ua=0.5400392317723339, err=0.0 ug[5,2]=1.0585488035662491, Ua=1.0585488035662491, err=0.0 ug[5,3]=1.534857375005895, Ua=1.534857375005895, err=0.0 ug[5,4]=1.9499760264265882, Ua=1.9499760264265882, err=0.0 ug[5,5]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=6, ny=6, npx=6, npy=6 maxerr=1.3316734979174072E-6, avgerr=2.547645210879159E-7 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=6, ny=6 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.2)=0.0 i=2, Ua(0.4)=0.0 i=3, Ua(0.6000000000000001)=0.0 i=4, Ua(0.8)=0.0 i=5, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.2)=0.19866933079506122 ii=2, Ua(0.4)=0.3894183423086505 ii=3, Ua(0.6000000000000001)=0.5646424733950355 ii=4, Ua(0.8)=0.7173560908995228 ii=5, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=8 xx[1]=0.019855071751231912, xx[2]=0.10166676129318658, wx[1]=0.05061426814518486, wx[2]=0.11119051722668723 calling gauleg ymin=0.0, ymax=1.0, npy=8 yy[1]=0.019855071751231912, yy[2]=0.10166676129318658, wy[1]=0.05061426814518486, wy[2]=0.11119051722668723 galk(xx[2],yy[2])=-518.467699268713 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=2.411683675775933E-4, rmserr=1.3519566320483663E-4, avgerr=1.0591916963244297E-4 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.19866933079506144, Ua=0.19866933079506122, err=2.220446049250313E-16 ug[0,2]=0.3894183423086521, Ua=0.3894183423086505, err=1.5543122344752192E-15 ug[0,3]=0.5646424733950355, Ua=0.5646424733950355, err=0.0 ug[0,4]=0.7173560908995232, Ua=0.7173560908995228, err=4.440892098500626E-16 ug[0,5]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=-7.067314969370479E-16, Ua=0.0, err=-7.067314969370479E-16 ug[1,1]=0.24265541436673024, Ua=0.24265526859492295, err=1.457718072916947E-7 ug[1,2]=0.4756358710370592, Ua=0.4756366373739469, err=-7.663368877253163E-7 ug[1,3]=0.6896548184592697, Ua=0.6896558743790767, err=-1.0559198070358988E-6 ug[1,4]=0.8761803471402912, Ua=0.8761807080076747, err=-3.608673834198939E-7 ug[1,5]=1.0277749817561195, Ua=1.0277749817561193, err=2.220446049250313E-16 ug[2,0]=-6.43041119774593E-16, Ua=0.0, err=-6.43041119774593E-16 ug[2,1]=0.2963805255416884, Ua=0.29637981434393573, err=7.111977526896851E-7 ug[2,2]=0.5809438892527273, Ua=0.5809439007705672, err=-1.1517839904051641E-8 ug[2,3]=0.8423476076344718, Ua=0.8423475871479679, err=2.048650393771112E-8 ug[2,4]=1.070170637440514, Ua=1.0701695334073043, err=1.1040332097422834E-6 ug[2,5]=1.255327197484942, Ua=1.2553271974849423, err=-2.220446049250313E-16 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=0.36199996842509546, Ua=0.3619991227026822, err=8.457224132674135E-7 ug[3,2]=0.7095664541720047, Ua=0.7095664827374989, err=-2.8565494192278607E-8 ug[3,3]=1.0288456699859978, Ua=1.028845666272092, err=3.7139058495228028E-9 ug[3,4]=1.3071093316259148, Ua=1.3071080198026634, err=1.3118232513598116E-6 ug[3,5]=1.5332601014015848, Ua=1.5332601014015848, err=0.0 ug[4,0]=-1.3312765603494319E-18, Ua=0.0, err=-1.3312765603494319E-18 ug[4,1]=0.4421471522041082, Ua=0.4421467269206178, err=4.252834904239222E-7 ug[4,2]=0.8666654919181999, Ua=0.8666664591135917, err=-9.671953918877207E-7 ug[4,3]=1.2566336028323732, Ua=1.256634934505871, err=-1.3316734976953626E-6 ug[4,4]=1.5965052591861255, Ua=1.5965053406002512, err=-8.141412566331496E-8 ug[4,5]=1.8727281168288372, Ua=1.8727281168288372, err=0.0 ug[5,0]=0.0, Ua=0.0, err=0.0 ug[5,1]=0.5400392317723339, Ua=0.5400392317723339, err=0.0 ug[5,2]=1.0585488035662491, Ua=1.0585488035662491, err=0.0 ug[5,3]=1.534857375005895, Ua=1.534857375005895, err=0.0 ug[5,4]=1.9499760264265882, Ua=1.9499760264265882, err=0.0 ug[5,5]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=6, ny=6, npx=8, npy=8 maxerr=1.3316734976953626E-6, avgerr=2.547645212805978E-7 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=8, ny=8 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.14285714285714285)=0.0 i=2, Ua(0.2857142857142857)=0.0 i=3, Ua(0.42857142857142855)=0.0 i=4, Ua(0.5714285714285714)=0.0 i=5, Ua(0.7142857142857142)=0.0 i=6, Ua(0.8571428571428571)=0.0 i=7, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.14285714285714285)=0.14237172979226365 ii=2, Ua(0.2857142857142857)=0.28184285212220994 ii=3, Ua(0.42857142857142855)=0.415571854993052 ii=4, Ua(0.5714285714285714)=0.5408342133588315 ii=5, Ua(0.7142857142857142)=0.6550778971785185 ii=6, Ua(0.8571428571428571)=0.7559753651467324 ii=7, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=6 xx[1]=0.033765242898423975, xx[2]=0.1693953067668677, wx[1]=0.08566224618958117, wx[2]=0.1803807865240693 calling gauleg ymin=0.0, ymax=1.0, npy=6 yy[1]=0.033765242898423975, yy[2]=0.1693953067668677, wy[1]=0.08566224618958117, wy[2]=0.1803807865240693 galk(xx[2],yy[2])=26.474321817787903 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=8.400920679108026E-7, rmserr=4.325748413723461E-7, avgerr=3.8725345008175064E-7 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=-3.1791605278502254E-17, Ua=0.0, err=-3.1791605278502254E-17 ug[0,1]=0.1423717297922633, Ua=0.14237172979226365, err=-3.3306690738754696E-16 ug[0,2]=0.2818428521222054, Ua=0.28184285212220994, err=-4.551914400963142E-15 ug[0,3]=0.4155718549930416, Ua=0.415571854993052, err=-1.0380585280245214E-14 ug[0,4]=0.5408342133588315, Ua=0.5408342133588315, err=0.0 ug[0,5]=0.6550778971785194, Ua=0.6550778971785185, err=8.881784197001252E-16 ug[0,6]=0.7559753651467275, Ua=0.7559753651467324, err=-4.884981308350689E-15 ug[0,7]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=-2.1316203312365899E-16, Ua=0.0, err=-2.1316203312365899E-16 ug[1,1]=0.16423504352034946, Ua=0.16423504375102027, err=-2.3067081578176385E-10 ug[1,2]=0.3251240494455198, Ua=0.3251240482695797, err=1.175940123054886E-9 ug[1,3]=0.4793891436234365, Ua=0.47938914478361044, err=-1.1601739569044867E-9 ug[1,4]=0.6238874154015589, Ua=0.6238874165723801, err=-1.1708212177552468E-9 ug[1,5]=0.7556749323418309, Ua=0.7556749311146356, err=1.2271953453435458E-9 ug[1,6]=0.872066717504929, Ua=0.8720667182363174, err=-7.313883942927646E-10 ug[1,7]=0.9706914722943022, Ua=0.9706914722943023, err=-1.1102230246251565E-16 ug[2,0]=6.146458755159816E-16, Ua=0.0, err=6.146458755159816E-16 ug[2,1]=0.18945579789534636, Ua=0.1894557974062435, err=4.891028693165822E-10 ug[2,2]=0.37505172324948033, Ua=0.3750517210823745, err=2.1671058281214073E-9 ug[2,3]=0.5530065369694285, Ua=0.5530065363550757, err=6.143527908619717E-10 ug[2,4]=0.7196946856904411, Ua=0.7196946845134395, err=1.1770016072887302E-9 ug[2,5]=0.871720151722714, Ua=0.8717201480536155, err=3.6690984694942586E-9 ug[2,6]=1.0059856421214157, Ua=1.005985639370471, err=2.7509448052853713E-9 ug[2,7]=1.1197557032819019, Ua=1.1197557032819017, err=2.220446049250313E-16 ug[3,0]=1.7198005797386989E-15, Ua=0.0, err=1.7198005797386989E-15 ug[3,1]=0.2185495753551604, Ua=0.21854957596778182, err=-6.126214258106444E-10 ug[3,2]=0.43264653765254274, Ua=0.4326465367157907, err=9.367520648062566E-10 ug[3,3]=0.6379289795730689, Ua=0.637928982287404, err=-2.7143350900260543E-9 ug[3,4]=0.8302145920706213, Ua=0.8302145950667821, err=-2.996160763935052E-9 ug[3,5]=1.0055858483818814, Ua=1.0055858481394315, err=2.424498379838269E-10 ug[3,6]=1.160469816536137, Ua=1.160469818944949, err=-2.4088120387233403E-9 ug[3,7]=1.2917109821401542, Ua=1.2917109821401545, err=-2.220446049250313E-16 ug[4,0]=0.0, Ua=0.0, err=0.0 ug[4,1]=0.2521111398640425, Ua=0.25211114048560224, err=-6.215597481151747E-10 ug[4,2]=0.49908590114114854, Ua=0.49908589991793717, err=1.2232113655308297E-9 ug[4,3]=0.7358925403233589, Ua=0.7358925431958107, err=-2.8724517209255396E-9 ug[4,4]=0.957706491988686, Ua=0.9577064951200566, err=-3.131370607256656E-9 ug[4,5]=1.1600086343770002, Ua=1.160008633775556, err=6.01444227754655E-10 ug[4,6]=1.3386773583610698, Ua=1.3386773607671567, err=-2.4060868852870954E-9 ug[4,7]=1.4900725725184618, Ua=1.490072572518462, err=-2.220446049250313E-16 ug[5,0]=0.0, Ua=0.0, err=0.0 ug[5,1]=0.2908265869723624, Ua=0.2908265864872735, err=4.850889134822012E-10 ug[5,2]=0.5757280265252934, Ua=0.5757280235910555, err=2.9342379637142812E-9 ug[5,3]=0.8488998780521733, Ua=0.8488998778350231, err=2.171501867209713E-10 ug[5,4]=1.1047766890071844, Ua=1.1047766881541794, err=8.530049999677658E-10 ug[5,5]=1.3381453583460878, Ua=1.33814535369958, err=4.646507845151859E-9 ug[5,6]=1.5442513456909863, Ua=1.5442513428395614, err=2.8514248739952563E-9 ug[5,7]=1.7188955595105995, Ua=1.7188955595105997, err=-2.220446049250313E-16 ug[6,0]=-2.9985154403462067E-15, Ua=0.0, err=-2.9985154403462067E-15 ug[6,1]=0.3354873692992184, Ua=0.3354873697565533, err=-4.5733489217880674E-10 ug[6,2]=0.6641396970234535, Ua=0.6641396945947863, err=2.4286672672957366E-9 ug[6,3]=0.979261181069331, Ua=0.979261183241216, err=-2.171885005175511E-9 ug[6,4]=1.274431712460559, Ua=1.2744317146308102, err=-2.1702510899501704E-9 ug[6,5]=1.5436376406990657, Ua=1.5436376381093682, err=2.589697567501048E-9 ug[6,6]=1.7813942912700598, Ua=1.781394292419482, err=-1.1494223350894117E-9 ug[6,7]=1.9828577473320683, Ua=1.9828577473320683, err=0.0 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=0.38700648598059156, Ua=0.38700648598059156, err=0.0 ug[7,2]=0.7661283034048733, Ua=0.7661283034048733, err=0.0 ug[7,3]=1.1296414218466306, Ua=1.1296414218466306, err=0.0 ug[7,4]=1.4701398143822542, Ua=1.4701398143822542, err=0.0 ug[7,5]=1.7806863441255298, Ua=1.7806863441255298, err=0.0 ug[7,6]=2.0549540978410543, Ua=2.0549540978410543, err=0.0 ug[7,7]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=8, ny=8, npx=6, npy=6 maxerr=4.646507845151859E-9, avgerr=9.419648836831521E-10 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0 nx=8, ny=8 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.14285714285714285)=0.0 i=2, Ua(0.2857142857142857)=0.0 i=3, Ua(0.42857142857142855)=0.0 i=4, Ua(0.5714285714285714)=0.0 i=5, Ua(0.7142857142857142)=0.0 i=6, Ua(0.8571428571428571)=0.0 i=7, Ua(1.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.14285714285714285)=0.14237172979226365 ii=2, Ua(0.2857142857142857)=0.28184285212220994 ii=3, Ua(0.42857142857142855)=0.415571854993052 ii=4, Ua(0.5714285714285714)=0.5408342133588315 ii=5, Ua(0.7142857142857142)=0.6550778971785185 ii=6, Ua(0.8571428571428571)=0.7559753651467324 ii=7, Ua(1.0)=0.8414709848078965 calling gauleg xmin=0.0, xmax=1.0, npx=8 xx[1]=0.019855071751231912, xx[2]=0.10166676129318658, wx[1]=0.05061426814518486, wx[2]=0.11119051722668723 calling gauleg ymin=0.0, ymax=1.0, npy=8 yy[1]=0.019855071751231912, yy[2]=0.10166676129318658, wy[1]=0.05061426814518486, wy[2]=0.11119051722668723 galk(xx[2],yy[2])=-852.5551080658661 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=1.0434178250307014E-6, rmserr=3.740495754656418E-7, avgerr=3.0379471605927283E-7 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.14237172979226317, Ua=0.14237172979226365, err=-4.718447854656915E-16 ug[0,2]=0.28184285212220833, Ua=0.28184285212220994, err=-1.609823385706477E-15 ug[0,3]=0.4155718549930513, Ua=0.415571854993052, err=-6.661338147750939E-16 ug[0,4]=0.5408342133588313, Ua=0.5408342133588315, err=-2.220446049250313E-16 ug[0,5]=0.6550778971785214, Ua=0.6550778971785185, err=2.886579864025407E-15 ug[0,6]=0.7559753651467326, Ua=0.7559753651467324, err=2.220446049250313E-16 ug[0,7]=0.8414709848078965, Ua=0.8414709848078965, err=0.0 ug[1,0]=-4.34847176477174E-15, Ua=0.0, err=-4.34847176477174E-15 ug[1,1]=0.16423504310541903, Ua=0.16423504375102027, err=-6.456012391353738E-10 ug[1,2]=0.325124048451371, Ua=0.3251240482695797, err=1.8179130423234824E-10 ug[1,3]=0.4793891439463346, Ua=0.47938914478361044, err=-8.372758597552377E-10 ug[1,4]=0.6238874154935092, Ua=0.6238874165723801, err=-1.0788708815212544E-9 ug[1,5]=0.7556749308359689, Ua=0.7556749311146356, err=-2.7866664531472907E-10 ug[1,6]=0.8720667168409592, Ua=0.8720667182363174, err=-1.3953582733705616E-9 ug[1,7]=0.9706914722942974, Ua=0.9706914722943023, err=-4.884981308350689E-15 ug[2,0]=1.7722624105850032E-15, Ua=0.0, err=1.7722624105850032E-15 ug[2,1]=0.18945579715153874, Ua=0.1894557974062435, err=-2.5470475728539554E-10 ug[2,2]=0.375051722225302, Ua=0.3750517210823745, err=1.1429274748842033E-9 ug[2,3]=0.5530065368116955, Ua=0.5530065363550757, err=4.566198530397969E-10 ug[2,4]=0.7196946851465972, Ua=0.7196946845134395, err=6.331576374307701E-10 ug[2,5]=0.8717201499032712, Ua=0.8717201480536155, err=1.8496556508651452E-9 ug[2,6]=1.0059856401314946, Ua=1.005985639370471, err=7.610236885113864E-10 ug[2,7]=1.1197557032819017, Ua=1.1197557032819017, err=0.0 ug[3,0]=6.908928706820206E-16, Ua=0.0, err=6.908928706820206E-16 ug[3,1]=0.21854957522632681, Ua=0.21854957596778182, err=-7.414550085016458E-10 ug[3,2]=0.4326465372749046, Ua=0.4326465367157907, err=5.591139218275032E-10 ug[3,3]=0.6379289816202272, Ua=0.637928982287404, err=-6.671768693067293E-10 ug[3,4]=0.830214594220094, Ua=0.8302145950667821, err=-8.466880530022536E-10 ug[3,5]=1.0055858484640352, Ua=1.0055858481394315, err=3.246036772708294E-10 ug[3,6]=1.16046981773311, Ua=1.160469818944949, err=-1.211838851489233E-9 ug[3,7]=1.2917109821401547, Ua=1.2917109821401545, err=2.220446049250313E-16 ug[4,0]=-1.7187800383995234E-15, Ua=0.0, err=-1.7187800383995234E-15 ug[4,1]=0.25211113963233434, Ua=0.25211114048560224, err=-8.53267900779997E-10 ug[4,2]=0.49908590058003827, Ua=0.49908589991793717, err=6.621010961715967E-10 ug[4,3]=0.7358925424369642, Ua=0.7358925431958107, err=-7.58846430137794E-10 ug[4,4]=0.9577064941553021, Ua=0.9577064951200566, err=-9.64754498511411E-10 ug[4,5]=1.1600086341781914, Ua=1.160008633775556, err=4.026354805120036E-10 ug[4,6]=1.3386773593831542, Ua=1.3386773607671567, err=-1.3840024681854857E-9 ug[4,7]=1.4900725725184618, Ua=1.490072572518462, err=-2.220446049250313E-16 ug[5,0]=3.0788982599127093E-15, Ua=0.0, err=3.0788982599127093E-15 ug[5,1]=0.29082658597188565, Ua=0.2908265864872735, err=-5.153878435137926E-10 ug[5,2]=0.5757280251102922, Ua=0.5757280235910555, err=1.5192367364136317E-9 ug[5,3]=0.8488998781691912, Ua=0.8488998778350231, err=3.3416813760567265E-10 ug[5,4]=1.1047766886398087, Ua=1.1047766881541794, err=4.856293145394375E-10 ug[5,5]=1.3381453559736565, Ua=1.33814535369958, err=2.274076482677856E-9 ug[5,6]=1.5442513433714298, Ua=1.5442513428395614, err=5.318683271582358E-10 ug[5,7]=1.7188955595105997, Ua=1.7188955595105997, err=0.0 ug[6,0]=-5.585206971658777E-16, Ua=0.0, err=-5.585206971658777E-16 ug[6,1]=0.33548736869537166, Ua=0.3354873697565533, err=-1.0611816425587506E-9 ug[6,2]=0.6641396953414463, Ua=0.6641396945947863, err=7.466600671079959E-10 ug[6,3]=0.9792611821541027, Ua=0.979261183241216, err=-1.087113288278374E-9 ug[6,4]=1.2744317132396774, Ua=1.2744317146308102, err=-1.3911327645388383E-9 ug[6,5]=1.5436376384282235, Ua=1.5436376381093682, err=3.188553865385302E-10 ug[6,6]=1.7813942905991715, Ua=1.781394292419482, err=-1.8203105689451604E-9 ug[6,7]=1.9828577473320683, Ua=1.9828577473320683, err=0.0 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=0.38700648598059156, Ua=0.38700648598059156, err=0.0 ug[7,2]=0.7661283034048733, Ua=0.7661283034048733, err=0.0 ug[7,3]=1.1296414218466306, Ua=1.1296414218466306, err=0.0 ug[7,4]=1.4701398143822542, Ua=1.4701398143822542, err=0.0 ug[7,5]=1.7806863441255298, Ua=1.7806863441255298, err=0.0 ug[7,6]=2.0549540978410543, Ua=2.0549540978410543, err=0.0 ug[7,7]=2.2873552871788427, Ua=2.2873552871788427, err=0.0 xmax=1.0, ymax=1.0, nx=8, ny=8, npx=8, npy=8 maxerr=2.274076482677856E-9, avgerr=4.840278383794778E-10 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=1.5, ymin=0.0, ymax=1.5 nx=8, ny=8 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.21428571428571427)=0.0 i=2, Ua(0.42857142857142855)=0.0 i=3, Ua(0.6428571428571428)=0.0 i=4, Ua(0.8571428571428571)=0.0 i=5, Ua(1.0714285714285714)=0.0 i=6, Ua(1.2857142857142856)=0.0 i=7, Ua(1.5)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.21428571428571427)=0.21264953365318406 ii=2, Ua(0.42857142857142855)=0.415571854993052 ii=3, Ua(0.6428571428571428)=0.5994847028790593 ii=4, Ua(0.8571428571428571)=0.7559753651467324 ii=5, Ua(1.0714285714285714)=0.877885500694737 ii=6, Ua(1.2857142857142856)=0.9596385829666849 ii=7, Ua(1.5)=0.9974949866040544 calling gauleg xmin=0.0, xmax=1.5, npx=8 xx[1]=0.029782607626847923, xx[2]=0.1525001419397799, wx[1]=0.0759214022177773, wx[2]=0.16678577584003085 calling gauleg ymin=0.0, ymax=1.5, npy=8 yy[1]=0.029782607626847923, yy[2]=0.1525001419397799, wy[1]=0.0759214022177773, wy[2]=0.16678577584003085 galk(xx[2],yy[2])=-378.91338136260697 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=2.2508470642890188E-5, rmserr=7.845606907275997E-6, avgerr=6.372403638832094E-6 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.21264953365317976, Ua=0.21264953365318406, err=-4.3021142204224816E-15 ug[0,2]=0.4155718549930431, Ua=0.415571854993052, err=-8.881784197001252E-15 ug[0,3]=0.5994847028790575, Ua=0.5994847028790593, err=-1.7763568394002505E-15 ug[0,4]=0.7559753651467322, Ua=0.7559753651467324, err=-1.1102230246251565E-16 ug[0,5]=0.877885500694737, Ua=0.877885500694737, err=0.0 ug[0,6]=0.9596385829666839, Ua=0.9596385829666849, err=-9.992007221626409E-16 ug[0,7]=0.9974949866040544, Ua=0.9974949866040544, err=0.0 ug[1,0]=-4.1059936091799E-15, Ua=0.0, err=-4.1059936091799E-15 ug[1,1]=0.2634677681954659, Ua=0.2634677956743828, err=-2.747891686416537E-8 ug[1,2]=0.5148838064100363, Ua=0.5148838029332505, err=3.4767857481909914E-9 ug[1,3]=0.742747479373932, Ua=0.7427475174512008, err=-3.807726878246598E-8 ug[1,4]=0.9366357380584769, Ua=0.9366357857345993, err=-4.7676122383322195E-8 ug[1,5]=1.087679574965765, Ua=1.0876795906816743, err=-1.571590924065447E-8 ug[1,6]=1.188969688546369, Ua=1.1889697463934927, err=-5.784712375778156E-8 ug[1,7]=1.2358729445672738, Ua=1.2358729445672738, err=0.0 ug[2,0]=1.1450604700891703E-15, Ua=0.0, err=1.1450604700891703E-15 ug[2,1]=0.3264304242835543, Ua=0.32643043304637376, err=-8.76281947004287E-9 ug[2,2]=0.637929033316787, Ua=0.637928982287404, err=5.102938294143655E-8 ug[2,3]=0.920246815072199, Ua=0.9202467920039941, err=2.30682049018327E-8 ug[2,4]=1.1604698494983146, Ua=1.160469818944949, err=3.055336561530453E-8 ug[2,5]=1.3476096380450544, Ua=1.3476095584779795, err=7.95670749287325E-8 ug[2,6]=1.4731057228772473, Ua=1.4731056909662446, err=3.191100272914582E-8 ug[2,7]=1.5312176558534079, Ua=1.531217655853405, err=2.886579864025407E-15 ug[3,0]=-1.0654787752752596E-14, Ua=0.0, err=-1.0654787752752596E-14 ug[3,1]=0.40443963377078884, Ua=0.4044396672697548, err=-3.349896593451973E-8 ug[3,2]=0.790379104543577, Ua=0.7903790799474819, err=2.4596095049567168E-8 ug[3,3]=1.1401642086344395, Ua=1.140164239255477, err=-3.0621037483413716E-8 ug[3,4]=1.4377949100697398, Ua=1.437794947825872, err=-3.775613222067875E-8 ug[3,5]=1.6696567207837887, Ua=1.669656705577286, err=1.5206502723685844E-8 ug[3,6]=1.8251434248946203, Ua=1.8251434768121986, err=-5.191757823652665E-8 ug[3,7]=1.8971428413445366, Ua=1.8971428413445366, err=0.0 ug[4,0]=-1.5270861193913625E-15, Ua=0.0, err=-1.5270861193913625E-15 ug[4,1]=0.5010912415258746, Ua=0.5010912828646478, err=-4.133877318235335E-8 ug[4,2]=0.979261214998613, Ua=0.979261183241216, err=3.175739693439539E-8 ug[4,3]=1.4126367726421785, Ua=1.4126368097911044, err=-3.714892593542629E-8 ug[4,4]=1.7813942465075285, Ua=1.781394292419482, err=-4.591195357228628E-8 ug[4,5]=2.0686656049725425, Ua=2.068665584138292, err=2.0834250324952563E-8 ug[4,6]=2.2613099915222206, Ua=2.2613100549256187, err=-6.340339808730278E-8 ug[4,7]=2.3505155826190354, Ua=2.3505155826190363, err=-8.881784197001252E-16 ug[5,0]=3.9384162057467425E-15, Ua=0.0, err=3.9384162057467425E-15 ug[5,1]=0.6208403457023782, Ua=0.6208403727012857, err=-2.6998907443065434E-8 ug[5,2]=1.2132817666055047, Ua=1.2132816889165459, err=7.768895882165339E-8 ug[5,3]=1.7502239625262084, Ua=1.7502239481566897, err=1.4369518686052629E-8 ug[5,4]=2.207105859607472, Ua=2.2071058393015206, err=2.0305951586863102E-8 ug[5,5]=2.563028356088057, Ua=2.563028246886609, err=1.0920144788428843E-7 ug[5,6]=2.8017102534171228, Ua=2.8017102378378502, err=1.5579272538701616E-8 ug[5,7]=2.912233799021324, Ua=2.912233799021324, err=0.0 ug[6,0]=1.3196243379274679E-15, Ua=0.0, err=1.3196243379274679E-15 ug[6,1]=0.7692066355514033, Ua=0.7692066925857598, err=-5.703435645987298E-8 ug[6,2]=1.503227662808469, Ua=1.5032276187930784, err=4.4015390665563814E-8 ug[6,3]=2.168486456055851, Ua=2.168486512222612, err=-5.6166761019937894E-8 ug[6,4]=2.7345524134925934, Ua=2.7345524831915053, err=-6.969891197528E-8 ug[6,5]=3.1755320436147025, Ua=3.175532016730013, err=2.688468958567114E-8 ug[6,6]=3.471253329795851, Ua=3.471253417773184, err=-8.797733297427612E-8 ug[6,7]=3.6081895235564403, Ua=3.6081895235564403, err=0.0 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=0.9530290907859614, Ua=0.9530290907859614, err=0.0 ug[7,2]=1.862463840462476, Ua=1.862463840462476, err=0.0 ug[7,3]=2.686704040727942, Ua=2.686704040727942, err=0.0 ug[7,4]=3.3880465314229378, Ua=3.3880465314229378, err=0.0 ug[7,5]=3.934409853471862, Ua=3.934409853471862, err=0.0 ug[7,6]=4.300801748756499, Ua=4.300801748756499, err=0.0 ug[7,7]=4.470462379180405, Ua=4.470462379180405, err=0.0 xmax=1.5, ymax=1.5, nx=8, ny=8, npx=8, npy=8 maxerr=1.0920144788428843E-7, avgerr=2.2735570769150244E-8 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=3.0, ymin=0.0, ymax=3.0 nx=8, ny=8 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.42857142857142855)=0.0 i=2, Ua(0.8571428571428571)=0.0 i=3, Ua(1.2857142857142856)=0.0 i=4, Ua(1.7142857142857142)=0.0 i=5, Ua(2.142857142857143)=0.0 i=6, Ua(2.571428571428571)=0.0 i=7, Ua(3.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.42857142857142855)=0.415571854993052 ii=2, Ua(0.8571428571428571)=0.7559753651467324 ii=3, Ua(1.2857142857142856)=0.9596385829666849 ii=4, Ua(1.7142857142857142)=0.9897230488598214 ii=5, Ua(2.142857142857143)=0.8407871057952504 ii=6, Ua(2.571428571428571)=0.5397701824006441 ii=7, Ua(3.0)=0.1411200080598672 calling gauleg xmin=0.0, xmax=3.0, npx=8 xx[1]=0.05956521525369585, xx[2]=0.3050002838795598, wx[1]=0.1518428044355546, wx[2]=0.3335715516800617 calling gauleg ymin=0.0, ymax=3.0, npy=8 yy[1]=0.05956521525369585, yy[2]=0.3050002838795598, wy[1]=0.1518428044355546, wy[2]=0.3335715516800617 galk(xx[2],yy[2])=-94.72834534065174 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=0.004677199616024197, rmserr=0.0017132293513180384, avgerr=0.001372166161557625 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.41557185499303984, Ua=0.415571854993052, err=-1.2156942119645464E-14 ug[0,2]=0.7559753651467005, Ua=0.7559753651467324, err=-3.186340080674199E-14 ug[0,3]=0.9596385829666827, Ua=0.9596385829666849, err=-2.220446049250313E-15 ug[0,4]=0.9897230488598214, Ua=0.9897230488598214, err=0.0 ug[0,5]=0.8407871057952505, Ua=0.8407871057952504, err=1.1102230246251565E-16 ug[0,6]=0.5397701824006398, Ua=0.5397701824006441, err=-4.3298697960381105E-15 ug[0,7]=0.1411200080598672, Ua=0.1411200080598672, err=0.0 ug[1,0]=-1.7623482989956718E-14, Ua=0.0, err=-1.7623482989956718E-14 ug[1,1]=0.6379097222404075, Ua=0.637928982287404, err=-1.9260046996483204E-5 ug[1,2]=1.1604611991659124, Ua=1.160469818944949, err=-8.619779036544983E-6 ug[1,3]=1.4730749677510744, Ua=1.4731056909662446, err=-3.072321517016974E-5 ug[1,4]=1.5192555650940216, Ua=1.5192872417119985, err=-3.167661797687238E-5 ug[1,5]=1.2906504975150597, Ua=1.2906611847650356, err=-1.0687249975882551E-5 ug[1,6]=0.8285590620835065, Ua=0.8285812405021662, err=-2.2178418659701826E-5 ug[1,7]=0.21662810423849932, Ua=0.21662810423849924, err=8.326672684688674E-17 ug[2,0]=1.1387184577145139E-14, Ua=0.0, err=1.1387184577145139E-14 ug[2,1]=0.9792628504548715, Ua=0.979261183241216, err=1.6672136554651829E-6 ug[2,2]=1.7814332674389834, Ua=1.781394292419482, err=3.8975019501341635E-5 ug[2,3]=2.261333767838436, Ua=2.2613100549256187, err=2.371291281733079E-5 ug[2,4]=2.3322262074728286, Ua=2.332201645185468, err=2.45622873604745E-5 ug[2,5]=1.9812880222161569, Ua=1.98124624221431, err=4.178000184684727E-5 ug[2,6]=1.2719298054939072, Ua=1.27192441245767, err=5.3930362371445995E-6 ug[2,7]=0.3325377895816081, Ua=0.3325377895816019, err=6.217248937900877E-15 ug[3,0]=-5.311630465076276E-14, Ua=0.0, err=-5.311630465076276E-14 ug[3,1]=1.5032033242547536, Ua=1.5032276187930784, err=-2.4294538324864945E-5 ug[3,2]=2.734567545111767, Ua=2.7345524831915053, err=1.506192026168307E-5 ug[3,3]=3.4712296724596325, Ua=3.471253417773184, err=-2.3745313551426506E-5 ug[3,4]=3.5800520570393024, Ua=3.5800764756483554, err=-2.441860905300075E-5 ug[3,5]=3.0413519811409793, Ua=3.0413378186490747, err=1.4162491904556873E-5 ug[3,6]=1.9524582417707381, Ua=1.9524841161324358, err=-2.5874361697653114E-5 ug[3,7]=0.5104664599662095, Ua=0.5104664599662095, err=0.0 ug[4,0]=-9.491306867074284E-15, Ua=0.0, err=-9.491306867074284E-15 ug[4,1]=2.3075123064778817, Ua=2.3075491121000464, err=-3.680562216468175E-5 ug[4,2]=4.197736152012968, Ua=4.1977103638142585, err=2.5788198709797427E-5 ug[4,3]=5.328557639764986, Ua=5.328592717374336, err=-3.5077609350508965E-5 ug[4,4]=5.495606875028156, Ua=5.49564296807255, err=-3.6093044394114315E-5 ug[4,5]=4.668669757668478, Ua=4.668645184057125, err=2.457361135288494E-5 ug[4,6]=2.9971470819421, Ua=2.9971861428332556, err=-3.9060891155351385E-5 ug[4,7]=0.7835981801595833, Ua=0.7835981801595838, err=-5.551115123125783E-16 ug[5,0]=1.8628342182187322E-14, Ua=0.0, err=1.8628342182187322E-14 ug[5,1]=3.5422067290138353, Ua=3.5422332840244857, err=-2.655501065040866E-5 ug[5,2]=6.443833638433895, Ua=6.443749903058499, err=8.37353753961878E-5 ug[5,3]=8.179734469510707, Ua=8.179725571828046, err=8.897682661768158E-6 ug[5,4]=8.436167651555182, Ua=8.436158232361684, err=9.419193498061418E-6 ug[5,5]=7.166751690416546, Ua=7.166664525383574, err=8.716503297190314E-5 ug[5,6]=4.600847104373782, Ua=4.600869579715633, err=-2.2475341850736186E-5 ug[5,7]=1.202872580482677, Ua=1.202872580482677, err=0.0 ug[6,0]=8.775694687287357E-15, Ua=0.0, err=8.775694687287357E-15 ug[6,1]=5.437482001953684, Ua=5.43755128445859, err=-6.928250490645382E-5 ug[6,2]=9.891625983757423, Ua=9.891562117076944, err=6.386668047930755E-5 ug[6,3]=12.556329240518492, Ua=12.55639415117215, err=-6.491065365743509E-5 ug[6,4]=12.949967662428914, Ua=12.950034442722236, err=-6.678029332185531E-5 ug[6,5]=11.00134389784858, Ua=11.001281612657866, err=6.228519071349581E-5 ug[6,6]=7.062552391735229, Ua=7.062624702229031, err=-7.231049380163057E-5 ug[6,7]=1.8464852031463173, Ua=1.8464852031463173, err=0.0 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=8.346983837700538, Ua=8.346983837700538, err=0.0 ug[7,2]=15.184171109674972, Ua=15.184171109674972, err=0.0 ug[7,3]=19.27485619109284, Ua=19.27485619109284, err=0.0 ug[7,4]=19.879118841603816, Ua=19.879118841603816, err=0.0 ug[7,5]=16.8876604579906, Ua=16.8876604579906, err=0.0 ug[7,6]=10.84157392864388, Ua=10.84157392864388, err=0.0 ug[7,7]=2.834471132487004, Ua=2.834471132487004, err=0.0 xmax=3.0, ymax=3.0, nx=8, ny=8, npx=8, npy=8 maxerr=8.716503297190314E-5, avgerr=1.9091804144384155E-5 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=3.0, ymin=0.0, ymax=3.0 nx=10, ny=10 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.3333333333333333)=0.0 i=2, Ua(0.6666666666666666)=0.0 i=3, Ua(1.0)=0.0 i=4, Ua(1.3333333333333333)=0.0 i=5, Ua(1.6666666666666665)=0.0 i=6, Ua(2.0)=0.0 i=7, Ua(2.333333333333333)=0.0 i=8, Ua(2.6666666666666665)=0.0 i=9, Ua(3.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.3333333333333333)=0.3271946967961522 ii=2, Ua(0.6666666666666666)=0.618369803069737 ii=3, Ua(1.0)=0.8414709848078965 ii=4, Ua(1.3333333333333333)=0.9719379013633127 ii=5, Ua(1.6666666666666665)=0.9954079577517649 ii=6, Ua(2.0)=0.9092974268256817 ii=7, Ua(2.333333333333333)=0.7230858817383248 ii=8, Ua(2.6666666666666665)=0.457272626635812 ii=9, Ua(3.0)=0.1411200080598672 calling gauleg xmin=0.0, xmax=3.0, npx=8 xx[1]=0.05956521525369585, xx[2]=0.3050002838795598, wx[1]=0.1518428044355546, wx[2]=0.3335715516800617 calling gauleg ymin=0.0, ymax=3.0, npy=8 yy[1]=0.05956521525369585, yy[2]=0.3050002838795598, wy[1]=0.1518428044355546, wy[2]=0.3335715516800617 galk(xx[2],yy[2])=-8.725178709831091 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=4.7058828816337606E-5, rmserr=1.6620041977403866E-5, avgerr=1.1924408800292083E-5 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=-1.996377542617286E-13, Ua=0.0, err=-1.996377542617286E-13 ug[0,1]=0.3271946967969625, Ua=0.3271946967961522, err=8.102962745226705E-13 ug[0,2]=0.6183698030692746, Ua=0.618369803069737, err=-4.624078897563777E-13 ug[0,3]=0.8414709848079087, Ua=0.8414709848078965, err=1.2212453270876722E-14 ug[0,4]=0.9719379013633127, Ua=0.9719379013633127, err=0.0 ug[0,5]=0.9954079577518771, Ua=0.9954079577517649, err=1.1213252548714081E-13 ug[0,6]=0.9092974268257172, Ua=0.9092974268256817, err=3.552713678800501E-14 ug[0,7]=0.7230858817383427, Ua=0.7230858817383248, err=1.787459069646502E-14 ug[0,8]=0.4572726266359076, Ua=0.457272626635812, err=9.564571357145724E-14 ug[0,9]=0.1411200080598672, Ua=0.1411200080598672, err=0.0 ug[1,0]=-5.6613618703936914E-14, Ua=0.0, err=-5.6613618703936914E-14 ug[1,1]=0.456636983840381, Ua=0.45663698427098576, err=-4.3060477405987285E-10 ug[1,2]=0.8630046380286839, Ua=0.8630045804621632, err=5.756652066146728E-8 ug[1,3]=1.1743675802077223, Ua=1.1743673617473285, err=2.1846039377493298E-7 ug[1,4]=1.3564486506506077, Ua=1.3564486115547374, err=3.9095870318917036E-8 ug[1,5]=1.3892037563336952, Ua=1.3892037138679325, err=4.246576268407409E-8 ug[1,6]=1.269027016848942, Ua=1.2690267869767307, err=2.298722112659135E-7 ug[1,7]=1.0091477120922059, Ua=1.0091476409583369, err=7.113386901735907E-8 ug[1,8]=0.6381753794027035, Ua=0.6381753593846915, err=2.0018012025779797E-8 ug[1,9]=0.19694883667670565, Ua=0.1969488366765998, err=1.0585976539800868E-13 ug[2,0]=2.3262834500835272E-14, Ua=0.0, err=2.3262834500835272E-14 ug[2,1]=0.6372882124785675, Ua=0.6372882490024289, err=-3.652386137975583E-8 ug[2,2]=1.204419919870473, Ua=1.2044199153992028, err=4.471270242945025E-9 ug[2,3]=1.6389618758653304, Ua=1.638961681670142, err=1.9419518837437977E-7 ug[2,4]=1.893076457281455, Ua=1.8930765362765658, err=-7.899511089703992E-8 ug[2,5]=1.9387898868849076, Ua=1.938789964049827, err=-7.71649193431756E-8 ug[2,6]=1.77106975196576, Ua=1.7710695516718034, err=2.002939567535833E-7 ug[2,7]=1.4083789960241357, Ua=1.4083789864677707, err=9.556365032636904E-9 ug[2,8]=0.8906454337862415, Ua=0.890645460941056, err=-2.715481450810131E-8 ug[2,9]=0.27486424357212835, Ua=0.2748642435721136, err=1.4765966227514582E-14 ug[3,0]=-6.983024456858818E-14, Ua=0.0, err=-6.983024456858818E-14 ug[3,1]=0.8894071387017495, Ua=0.8894073986691476, err=-2.5996739816402936E-7 ug[3,2]=1.6809030829014115, Ua=1.6809033989522646, err=-3.16050853044203E-7 ug[3,3]=2.2873552420427243, Ua=2.2873552871788427, err=-4.513611839840337E-8 ug[3,4]=2.6420005042154093, Ua=2.642001135666513, err=-6.314511038496562E-7 ug[3,5]=2.705798723323123, Ua=2.705799363460152, err=-6.401370291619912E-7 ug[3,6]=2.4717266000044686, Ua=2.471726672004819, err=-7.200035057053356E-8 ug[3,7]=1.9655508528311918, Ua=1.9655512127445747, err=-3.599133828746659E-7 ug[3,8]=1.2429955567076967, Ua=1.2429958716358653, err=-3.1492816865430484E-7 ug[3,9]=0.3836039535411664, Ua=0.3836039535411311, err=3.530509218307998E-14 ug[4,0]=0.0, Ua=0.0, err=0.0 ug[4,1]=1.2412680393327493, Ua=1.2412680165461594, err=2.2786589948253777E-8 ug[4,2]=2.345889831724343, Ua=2.34588966894722, err=1.6277712289181068E-7 ug[4,3]=3.1922620088128912, Ua=3.1922614593731526, err=5.494397385952254E-7 ug[4,4]=3.687209697020201, Ua=3.687209612027744, err=8.499245662818566E-8 ug[4,5]=3.776247305184267, Ua=3.7762472114350194, err=9.374924747618252E-8 ug[4,6]=3.449573030546678, Ua=3.4495724548666145, err=5.756800636191883E-7 ug[4,7]=2.743147887734333, Ua=2.7431476946493594, err=1.930849737874496E-7 ug[4,8]=1.7347405431337393, Ua=1.7347404827857276, err=6.034801169896298E-8 ug[4,9]=0.53536244387415, Ua=0.5353624438741494, err=5.551115123125783E-16 ug[5,0]=-7.577754550294542E-16, Ua=0.0, err=-7.577754550294542E-16 ug[5,1]=1.7323290394669046, Ua=1.7323290667537856, err=-2.7286880976973293E-8 ug[5,2]=3.2739528996732266, Ua=3.2739527698638335, err=1.2980939301243666E-7 ug[5,3]=4.455160414660921, Ua=4.455159756824624, err=6.578362965470319E-7 ug[5,4]=5.145915518751982, Ua=5.14591554844278, err=-2.9690797376247247E-8 ug[5,5]=5.270177507559858, Ua=5.27017752847541, err=-2.0915552845224283E-8 ug[5,6]=4.814266863432043, Ua=4.81426617924657, err=6.841854727213104E-7 ug[5,7]=3.8283711638157345, Ua=3.8283710064989083, err=1.5731682623254528E-7 ug[5,8]=2.421025380037002, Ua=2.4210253720756025, err=7.961399539624381E-9 ug[5,9]=0.7471584785952201, Ua=0.7471584785952172, err=2.886579864025407E-15 ug[6,0]=3.573541433951915E-16, Ua=0.0, err=3.573541433951915E-16 ug[6,1]=2.4176595046351808, Ua=2.4176599698993733, err=-4.6526419250625395E-7 ug[6,2]=4.569168719498665, Ua=4.569169164766985, err=-4.452683199929197E-7 ug[6,3]=6.217676679664519, Ua=6.217676312367968, err=3.672965513956683E-7 ug[6,4]=7.18170264723913, Ua=7.181703677850443, err=-1.0306113127356298E-6 ug[6,5]=7.355124201724, Ua=7.355125241149782, err=-1.039425781890202E-6 ug[6,6]=6.7188500381251375, Ua=6.71884969742825, err=3.4069688759075234E-7 ug[6,7]=5.34292164615304, Ua=5.342922144509216, err=-4.983561758820088E-7 ug[6,8]=3.378812560761865, Ua=3.378813090717385, err=-5.299555199123063E-7 ug[6,9]=1.042743656235877, Ua=1.0427436562359045, err=-2.7533531010703882E-14 ug[7,0]=-1.1307257146932082E-14, Ua=0.0, err=-1.1307257146932082E-14 ug[7,1]=3.3741159986419187, Ua=3.3741162936248252, err=-2.9498290654572656E-7 ug[7,2]=6.376789149835263, Ua=6.3767892586690325, err=-1.0883376955206359E-7 ug[7,3]=8.677467246572201, Ua=8.67746631670419, err=9.298680101466061E-7 ug[7,4]=10.022874333307277, Ua=10.02287488609454, err=-5.527872630750608E-7 ug[7,5]=10.264903626898592, Ua=10.264904174612953, err=-5.477143609766699E-7 ug[7,6]=9.376911065833555, Ua=9.376910120016776, err=9.458167795628469E-7 ug[7,7]=7.456648426382139, Ua=7.4566485311446735, err=-1.0476253464730689E-7 ug[7,8]=4.715513247267051, Ua=4.715513531448713, err=-2.84181662202343E-7 ug[7,9]=1.4552660028225257, Ua=1.4552660028225257, err=0.0 ug[8,0]=0.0, Ua=0.0, err=0.0 ug[8,1]=4.708958125546725, Ua=4.708958623068232, err=-4.975215066593819E-7 ug[8,2]=8.899526129675248, Ua=8.899526321554017, err=-1.9187876887372113E-7 ug[8,3]=12.110381175631005, Ua=12.110379809858395, err=1.3657726096738543E-6 ug[8,4]=13.988048029904895, Ua=13.988048726116867, err=-6.962119716291681E-7 ug[8,5]=14.325827118541007, Ua=14.32582780840791, err=-6.898669031585314E-7 ug[8,6]=13.086533661718097, Ua=13.08653227241091, err=1.389307186627775E-6 ug[8,7]=10.406591156446625, Ua=10.406591339565448, err=-1.831188232159775E-7 ug[8,8]=6.581028795420808, Ua=6.581029275151409, err=-4.797306010217994E-7 ug[8,9]=2.0309873153444853, Ua=2.0309873153444853, err=0.0 ug[9,0]=0.0, Ua=0.0, err=0.0 ug[9,1]=6.571881163570309, Ua=6.571881163570309, err=0.0 ug[9,2]=12.420289511741489, Ua=12.420289511741489, err=0.0 ug[9,3]=16.901396535150095, Ua=16.901396535150095, err=0.0 ug[9,4]=19.52189460487835, Ua=19.52189460487835, err=0.0 ug[9,5]=19.993303289057906, Ua=19.993303289057906, err=0.0 ug[9,6]=18.263727040666765, Ua=18.263727040666765, err=0.0 ug[9,7]=14.523568176290834, Ua=14.523568176290834, err=0.0 ug[9,8]=9.18456622625661, Ua=9.18456622625661, err=0.0 ug[9,9]=2.834471132487004, Ua=2.834471132487004, err=0.0 xmax=3.0, ymax=3.0, nx=10, ny=10, npx=8, npy=8 maxerr=1.389307186627775E-6, avgerr=2.1384076453912602E-7 laphi instantiated fem_laplace_la.java running Given: uxx+uyy=0 xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp(x)*sim(y) xmin=0.0, xmax=3.0, ymin=0.0, ymax=6.3 nx=10, ny=10 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.3333333333333333)=0.0 i=2, Ua(0.6666666666666666)=0.0 i=3, Ua(1.0)=0.0 i=4, Ua(1.3333333333333333)=0.0 i=5, Ua(1.6666666666666665)=0.0 i=6, Ua(2.0)=0.0 i=7, Ua(2.333333333333333)=0.0 i=8, Ua(2.6666666666666665)=0.0 i=9, Ua(3.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.7)=0.644217687237691 ii=2, Ua(1.4)=0.9854497299884601 ii=3, Ua(2.0999999999999996)=0.8632093666488739 ii=4, Ua(2.8)=0.3349881501559051 ii=5, Ua(3.5)=-0.35078322768961984 ii=6, Ua(4.199999999999999)=-0.8715757724135877 ii=7, Ua(4.8999999999999995)=-0.9824526126243326 ii=8, Ua(5.6)=-0.6312666378723216 ii=9, Ua(6.3)=0.016813900484349713 calling gauleg xmin=0.0, xmax=3.0, npx=8 xx[1]=0.05956521525369585, xx[2]=0.3050002838795598, wx[1]=0.1518428044355546, wx[2]=0.3335715516800617 calling gauleg ymin=0.0, ymax=6.3, npy=8 yy[1]=0.1250869520327611, yy[2]=0.6405005961470756, wy[1]=0.31886988931466465, wy[2]=0.7005002585281295 galk(xx[2],yy[2])=-5.351838641744471 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above check solution against PDE Uxx + Uyy = 0 maxerr=0.002722697705169849, rmserr=7.520822123361354E-4, avgerr=5.009487518498979E-4 writing fem_laplace_la.dat finished writing fem_laplace_la.dat ug computed Galerkin, Ua analytic, error ug[0,0]=-5.237554727249312E-13, Ua=0.0, err=-5.237554727249312E-13 ug[0,1]=0.6442176872375089, Ua=0.644217687237691, err=-1.8207657603852567E-13 ug[0,2]=0.9854497299885105, Ua=0.9854497299884601, err=5.040412531798211E-14 ug[0,3]=0.8632093666487626, Ua=0.8632093666488739, err=-1.113553693699032E-13 ug[0,4]=0.33498815015588973, Ua=0.3349881501559051, err=-1.5376588891058418E-14 ug[0,5]=-0.350783227689547, Ua=-0.35078322768961984, err=7.283063041541027E-14 ug[0,6]=-0.8715757724131938, Ua=-0.8715757724135877, err=3.9390712913700554E-13 ug[0,7]=-0.9824526126242696, Ua=-0.9824526126243326, err=6.294964549624638E-14 ug[0,8]=-0.631266637872377, Ua=-0.6312666378723216, err=-5.540012892879531E-14 ug[0,9]=0.01681390048502294, Ua=0.016813900484349713, err=6.732288337918391E-13 ug[1,0]=-2.779853294117347E-14, Ua=0.0, err=-2.779853294117347E-14 ug[1,1]=0.8990607344075757, Ua=0.8990782087691459, err=-1.7474361570180008E-5 ug[1,2]=1.375288348221412, Ua=1.375305887469627, err=-1.7539248214903935E-5 ug[1,3]=1.2047273172841158, Ua=1.2047057175458624, err=2.1599738253330614E-5 ug[1,4]=0.4675207451126696, Ua=0.46751362461418583, err=7.120498483781379E-6 ug[1,5]=-0.489562572967082, Ua=-0.48955743107543626, err=-5.141891645743524E-6 ug[1,6]=-1.2164062482142317, Ua=-1.216381977384409, err=-2.4270829822814477E-5 ug[1,7]=-1.371104888171849, Ua=-1.3711230732368094, err=1.8185064960318797E-5 ug[1,8]=-0.8809847680729069, Ua=-0.8810035633569331, err=1.8795284026151826E-5 ug[1,9]=0.023465688429961436, Ua=0.023465688430119477, err=-1.5804024755539103E-13 ug[2,0]=-2.2861179514839618E-14, Ua=0.0, err=-2.2861179514839618E-14 ug[2,1]=1.254740057746836, Ua=1.2547647192823652, err=-2.4661535529268974E-5 ug[2,2]=1.9193642488582283, Ua=1.9193939848466626, err=-2.9735988434254068E-5 ug[2,3]=1.6813368369376727, Ua=1.6813022679792584, err=3.456895841424945E-5 ug[2,4]=0.6524818429957252, Ua=0.6524678234085916, err=1.4019587133651257E-5 ug[2,5]=-0.683243349391448, Ua=-0.6832324336021056, err=-1.0915789342424986E-5 ug[2,6]=-1.6976363121158105, Ua=-1.6975978012884676, err=-3.8510827342852494E-5 ug[2,7]=-1.913525770269776, Ua=-1.9135563973315153, err=3.062706173917462E-5 ug[2,8]=-1.2295130154442444, Ua=-1.2295395195660557, err=2.6504121811266046E-5 ug[2,9]=0.03274900633625018, Ua=0.03274900633627364, err=-2.346040028911034E-14 ug[3,0]=1.1548969809751384E-14, Ua=0.0, err=1.1548969809751384E-14 ug[3,1]=1.751127635472289, Ua=1.7511652327901284, err=-3.7597317839477284E-5 ug[3,2]=2.6786857965087734, Ua=2.6787300938875043, err=-4.4297378730906445E-5 ug[3,3]=2.3464972001584914, Ua=2.3464463355172755, err=5.0864641215842E-5 ug[3,4]=0.9106124291107163, Ua=0.9105922013179071, err=2.022779280919096E-5 ug[3,5]=-0.9535433097430727, Ua=-0.9535276735569055, err=-1.5636186167178323E-5 ug[3,6]=-2.369245305788455, Ua=-2.3691885842770124, err=-5.6721511442425765E-5 ug[3,7]=-2.6705374642641697, Ua=-2.670583084218837, err=4.56199546672309E-5 ug[3,8]=-1.7159202968636706, Ua=-1.7159606306407686, err=4.033377709800057E-5 ug[3,9]=0.04570492015214923, Ua=0.04570492015212657, err=2.26554885962571E-14 ug[4,0]=-9.211949326394819E-15, Ua=0.0, err=-9.211949326394819E-15 ug[4,1]=2.4439022409262465, Ua=2.443947957260677, err=-4.571633443051226E-5 ug[4,2]=3.7384095817151426, Ua=3.7384690024814273, err=-5.942076628473458E-5 ug[4,3]=3.274796920587005, Ua=3.2747296606456326, err=6.725994137246616E-5 ug[4,4]=1.2708625133593663, Ua=1.2708337903457647, err=2.872301360157259E-5 ug[4,5]=-1.3307778601989892, Ua=-1.3307550688794498, err=-2.2791319539416932E-5 ug[4,6]=-3.3065438850600497, Ua=-3.3064690255891196, err=-7.485947093011092E-5 ug[4,7]=-3.727037814292712, Ua=-3.727098934560539, err=6.112026782689739E-5 ug[4,8]=-2.394766747560668, Ua=-2.394815977080818, err=4.922952014974058E-5 ug[4,9]=0.06378635445187253, Ua=0.06378635445187543, err=-2.9004576518332215E-15 ug[5,0]=-1.2959072046971068E-14, Ua=0.0, err=-1.2959072046971068E-14 ug[5,1]=3.4107392328961974, Ua=3.4108041354167677, err=-6.49025205703424E-5 ug[5,2]=5.2173726189886205, Ua=5.217453790662279, err=-8.117167365817579E-5 ug[5,3]=4.570344633195085, Ua=4.570253403194998, err=9.123000008681714E-5 ug[5,4]=1.77362817135256, Ua=1.7735914280257996, err=3.674332676029124E-5 ug[5,5]=-1.8572469672001397, Ua=-1.857218308874455, err=-2.865832568477167E-5 ug[5,6]=-4.61465127418165, Ua=-4.61454925527447, err=-1.0201890717986828E-4 ug[5,7]=-5.201501906373068, Ua=-5.201585582597814, err=8.367622474647618E-5 ug[5,8]=-3.3421649075302997, Ua=-3.3422349334086734, err=7.002587837368068E-5 ug[5,9]=0.0890210288239865, Ua=0.08902102882398275, err=3.760880495917718E-15 ug[6,0]=0.0, Ua=0.0, err=0.0 ug[6,1]=4.760060590332523, Ua=4.760160630922659, err=-1.0004059013635214E-4 ug[6,2]=7.281433836913891, Ua=7.2815433375607945, err=-1.0950064690362638E-4 ug[6,3]=6.378427030421616, Ua=6.378302435290926, err=1.24595130690075E-4 ug[6,4]=2.4752885562550118, Ua=2.475246233978987, err=4.232227602463112E-5 ug[6,5]=-2.5919879711496816, Ua=-2.5919569479625646, err=-3.102318711700747E-5 ug[6,6]=-6.440262829836503, Ua=-6.440122276832813, err=-1.4055300368998047E-4 ug[6,7]=-7.259284043630034, Ua=-7.2593974692221765, err=1.1342559214266856E-4 ug[6,8]=-4.6643566301740425, Ua=-4.664464600621924, err=1.0797044788191101E-4 ug[6,9]=0.1242388539206856, Ua=0.12423885392069726, err=-1.1671219546371958E-14 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=6.643203179611536, Ua=6.6433393219212995, err=-1.3614230976344288E-4 ug[7,2]=10.162079512461357, Ua=10.162212355702675, err=-1.3284324131745961E-4 ug[7,3]=8.901794336752346, Ua=8.901638129648877, err=1.5620710346908595E-4 ug[7,4]=3.4545283408984973, Ua=3.454484399288623, err=4.3941609874309506E-5 ug[7,5]=-3.6173968334679123, Ua=-3.6173673218647724, err=-2.951160313990897E-5 ug[7,6]=-8.988092314672958, Ua=-8.987914668621587, err=-1.776460513713829E-4 ug[7,7]=-10.131166927345033, Ua=-10.131305306684979, err=1.3837933994587104E-4 ug[7,8]=-6.509637526608115, Ua=-6.5097847530021795, err=1.4722639406450355E-4 ug[7,9]=0.17338928821018065, Ua=0.17338928821018065, err=0.0 ug[8,0]=0.0, Ua=0.0, err=0.0 ug[8,1]=9.27133838580539, Ua=9.271526901736364, err=-1.885159309740203E-4 ug[8,2]=14.182374337252122, Ua=14.182509829982035, err=-1.3549272991220107E-4 ug[8,3]=12.423415733689298, Ua=12.423236777358072, err=1.7895633122577692E-4 ug[8,4]=4.821148138022221, Ua=4.821121349913259, err=2.678810896217243E-5 ug[8,5]=-5.048452330845724, Ua=-5.048442780494869, err=-9.550350855036527E-6 ug[8,6]=-12.543851490095907, Ua=-12.543645387141812, err=-2.0610295409539958E-4 ug[8,7]=-14.139232666356307, Ua=-14.139375568350195, err=1.429019938878895E-4 ug[8,8]=-9.084933173771876, Ua=-9.085136485925824, err=2.0331215394797653E-4 ug[8,9]=0.2419842450029612, Ua=0.2419842450029612, err=0.0 ug[9,0]=0.0, Ua=0.0, err=0.0 ug[9,1]=12.939458143583208, Ua=12.939458143583208, err=0.0 ug[9,2]=19.793286937628533, Ua=19.793286937628533, err=0.0 ug[9,3]=17.3380236062674, Ua=17.3380236062674, err=0.0 ug[9,4]=6.728416858786766, Ua=6.728416858786766, err=0.0 ug[9,5]=-7.045669471794806, Ua=-7.045669471794806, err=0.0 ug[9,6]=-17.506067358168927, Ua=-17.506067358168927, err=0.0 ug[9,7]=-19.733088226148222, Ua=-19.733088226148222, err=0.0 ug[9,8]=-12.679329363361054, Ua=-12.679329363361054, err=0.0 ug[9,9]=0.3377162190012092, Ua=0.3377162190012092, err=0.0 xmax=3.0, ymax=6.3, nx=10, ny=10, npx=8, npy=8 maxerr=2.0610295409539958E-4, avgerr=4.441465921731336E-5