laphi instantiated fem_laplace2_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=2.0, ymin=0.0, ymax=6.3 nx=4, ny=4 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.6666666666666666)=0.0 i=2, Ua(1.3333333333333333)=0.0 i=3, Ua(2.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(2.1)=0.8632093666488737 ii=2, Ua(4.2)=-0.8715757724135882 ii=3, Ua(6.300000000000001)=0.0168139004843506 calling gauleg xmin=0.0, xmax=2.0, npx=3 xx[1]=0.2254033307585166, xx[2]=1.0, wx[1]=0.5555555555555527, wx[2]=0.8888888888888888 calling gauleg ymin=0.0, ymax=6.3, npy=3 yy[1]=0.7100204918893271, yy[2]=3.15, wy[1]=1.7499999999999911, wy[2]=2.8 galk(xx[2],yy[2])=-0.22040480010363503 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above writing fem_laplace2_la.dat finished writing fem_laplace2_la.dat check solution nu against PDE Uxx + Uyy = 0 nu maxerr=2.7811532012320512, rmserr=2.1462106363897817, avgerr=2.0018914570629853 check solution against PDE Uxx + Uyy = 0 maxerr=2.7811532012320543, rmserr=2.1462106363897826, avgerr=2.001891457062986 ug computed Galerkin, Ua analytic, error ug[0,0]=7.081338221682691E-16, Ua=0.0, err=7.081338221682691E-16 ug[0,1]=0.8632093666488737, Ua=0.8632093666488737, err=0.0 ug[0,2]=-0.8715757724135882, Ua=-0.8715757724135882, err=0.0 ug[0,3]=0.0168139004843506, Ua=0.0168139004843506, err=0.0 ug[1,0]=2.511236480443644E-15, Ua=0.0, err=2.511236480443644E-15 ug[1,1]=1.3656897445151397, Ua=1.681302267979258, err=-0.3156125234641183 ug[1,2]=-1.3821263132244166, Ua=-1.6975978012884685, err=0.3154714880640519 ug[1,3]=0.032749006336275366, Ua=0.032749006336275366, err=0.0 ug[2,0]=0.0, Ua=0.0, err=0.0 ug[2,1]=2.8274009193912977, Ua=3.2747296606456318, err=-0.4473287412543341 ug[2,2]=-2.8592441631296115, Ua=-3.3064690255891214, err=0.4472248624595099 ug[2,3]=0.0637863544518788, Ua=0.0637863544518788, err=0.0 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=6.378302435290924, Ua=6.378302435290924, err=0.0 ug[3,2]=-6.440122276832816, Ua=-6.440122276832816, err=0.0 ug[3,3]=0.12423885392070383, Ua=0.12423885392070383, err=0.0 xmax=2.0, ymax=6.3, nx=4, ny=4, npx=3, npy=3 maxerr=0.4473287412543341, avgerr=0.09535235095262609 fem_laplace2_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=2.0, ymin=0.0, ymax=6.3 nx=4, ny=4 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.6666666666666666)=0.0 i=2, Ua(1.3333333333333333)=0.0 i=3, Ua(2.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(2.1)=0.8632093666488737 ii=2, Ua(4.2)=-0.8715757724135882 ii=3, Ua(6.300000000000001)=0.0168139004843506 calling gauleg xmin=0.0, xmax=2.0, npx=4 xx[1]=0.13886368840594743, xx[2]=0.6600189564151437, wx[1]=0.3478548451374476, wx[2]=0.6521451548625464 calling gauleg ymin=0.0, ymax=6.3, npy=4 yy[1]=0.43742061847873437, yy[2]=2.0790597127077026, wy[1]=1.0957427621829599, wy[2]=2.054257237817021 galk(xx[2],yy[2])=-5.101659282185413 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above writing fem_laplace2_la.dat finished writing fem_laplace2_la.dat check solution nu against PDE Uxx + Uyy = 0 nu maxerr=1.4119453677188554, rmserr=1.111890070076541, avgerr=1.0547969270450717 check solution against PDE Uxx + Uyy = 0 maxerr=1.4119453677188547, rmserr=1.1118900700765406, avgerr=1.0547969270450714 ug computed Galerkin, Ua analytic, error ug[0,0]=0.0, Ua=0.0, err=0.0 ug[0,1]=0.8632093666488737, Ua=0.8632093666488737, err=0.0 ug[0,2]=-0.8715757724135912, Ua=-0.8715757724135882, err=-2.9976021664879227E-15 ug[0,3]=0.0168139004843506, Ua=0.0168139004843506, err=0.0 ug[1,0]=0.0, Ua=0.0, err=0.0 ug[1,1]=1.6321147176901325, Ua=1.681302267979258, err=-0.04918755028912547 ug[1,2]=-1.6485260414407326, Ua=-1.6975978012884685, err=0.04907175984773593 ug[1,3]=0.032749006336275366, Ua=0.032749006336275366, err=0.0 ug[2,0]=0.0, Ua=0.0, err=0.0 ug[2,1]=3.207396821028303, Ua=3.2747296606456318, err=-0.06733283961732894 ug[2,2]=-3.2392653097252895, Ua=-3.3064690255891214, err=0.06720371586383189 ug[2,3]=0.0637863544518788, Ua=0.0637863544518788, err=0.0 ug[3,0]=0.0, Ua=0.0, err=0.0 ug[3,1]=6.378302435290924, Ua=6.378302435290924, err=0.0 ug[3,2]=-6.440122276832816, Ua=-6.440122276832816, err=0.0 ug[3,3]=0.12423885392070383, Ua=0.12423885392070383, err=0.0 xmax=2.0, ymax=6.3, nx=4, ny=4, npx=4, npy=4 maxerr=0.06733283961732894, avgerr=0.014549741601126577 fem_laplace2_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=2.0, ymin=0.0, ymax=6.3 nx=6, ny=6 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.4)=0.0 i=2, Ua(0.8)=0.0 i=3, Ua(1.2000000000000002)=0.0 i=4, Ua(1.6)=0.0 i=5, Ua(2.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(1.26)=0.9520903415905158 ii=2, Ua(2.52)=0.5823306495240819 ii=3, Ua(3.7800000000000002)=-0.5959172238077642 ii=4, Ua(5.04)=-0.9468137755926089 ii=5, Ua(6.3)=0.016813900484349713 calling gauleg xmin=0.0, xmax=2.0, npx=6 xx[1]=0.06753048579684795, xx[2]=0.3387906135337354, wx[1]=0.17132449237916234, wx[2]=0.3607615730481386 calling gauleg ymin=0.0, ymax=6.3, npy=6 yy[1]=0.21272103026007105, yy[2]=1.0671904326312665, wy[1]=0.5396721509943614, wy[2]=1.1363989551016365 galk(xx[2],yy[2])=-24.043738112014953 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above writing fem_laplace2_la.dat finished writing fem_laplace2_la.dat check solution nu against PDE Uxx + Uyy = 0 nu maxerr=0.32695508605698426, rmserr=0.1883619373609654, avgerr=0.1675579479132256 check solution against PDE Uxx + Uyy = 0 maxerr=0.32695508605639395, rmserr=0.18836193736084836, avgerr=0.1675579479131352 ug computed Galerkin, Ua analytic, error ug[0,0]=-1.116795702715212E-15, Ua=0.0, err=-1.116795702715212E-15 ug[0,1]=0.9520903415905221, Ua=0.9520903415905158, err=6.328271240363392E-15 ug[0,2]=0.5823306495240818, Ua=0.5823306495240819, err=-1.1102230246251565E-16 ug[0,3]=-0.5959172238077628, Ua=-0.5959172238077642, err=1.4432899320127035E-15 ug[0,4]=-0.946813775592609, Ua=-0.9468137755926089, err=-1.1102230246251565E-16 ug[0,5]=0.016813900484349713, Ua=0.016813900484349713, err=0.0 ug[1,0]=-1.8988879962408686E-16, Ua=0.0, err=-1.8988879962408686E-16 ug[1,1]=1.4242921894868068, Ua=1.420351885970445, err=0.003940303516361876 ug[1,2]=0.8567396529195994, Ua=0.868735245153508, err=-0.011995592233908559 ug[1,3]=-0.8766996320807346, Ua=-0.8890040322262431, err=0.012304400145508487 ug[1,4]=-1.4168242188641063, Ua=-1.4124801744960334, err=-0.004344044368072897 ug[1,5]=0.025083392006235418, Ua=0.025083392006235418, err=0.0 ug[2,0]=-2.0619132566491246E-15, Ua=0.0, err=-2.0619132566491246E-15 ug[2,1]=2.12594205659603, Ua=2.1189160228320674, err=0.0070260337639624915 ug[2,2]=1.2757180875200038, Ua=1.296000694431447, err=-0.020282606911443235 ug[2,3]=-1.3054315300244188, Ua=-1.3262381715777853, err=0.020806641553366534 ug[2,4]=-2.1148887599081636, Ua=-2.107172809241834, err=-0.007715950666329796 ug[2,5]=0.03742002369551962, Ua=0.03742002369551962, err=0.0 ug[3,0]=-3.5147495734005423E-16, Ua=0.0, err=-3.5147495734005423E-16 ug[3,1]=3.1702069530195174, Ua=3.161051255088692, err=0.00915569793082538 ug[3,2]=1.9072405659577893, Ua=1.93340584411307, err=-0.02616527815528058 ug[3,3]=-1.9517093879618181, Ua=-1.9785148593143411, err=0.02680547135252298 ug[3,4]=-3.153539775369362, Ua=-3.1435324390251056, err=-0.010007336344256323 ug[3,5]=0.05582411553529772, Ua=0.05582411553529772, err=0.0 ug[4,0]=0.0, Ua=0.0, err=0.0 ug[4,1]=4.724322793591029, Ua=4.7157343328512455, err=0.008588460739783699 ug[4,2]=2.8592873482582863, Ua=2.884302588811845, err=-0.025015240553558638 ug[4,3]=-2.926026428791275, Ua=-2.951597331775377, err=0.025570902984101807 ug[4,4]=-4.698935646048293, Ua=-4.689599330374152, err=-0.009336315674140394 ug[4,5]=0.08327979427953686, Ua=0.08327979427953686, err=0.0 ug[5,0]=0.0, Ua=0.0, err=0.0 ug[5,1]=7.035048945262367, Ua=7.035048945262367, err=0.0 ug[5,2]=4.302873837460164, Ua=4.302873837460164, err=0.0 ug[5,3]=-4.403265797034582, Ua=-4.403265797034582, err=0.0 ug[5,4]=-6.996060103094123, Ua=-6.996060103094123, err=0.0 ug[5,5]=0.12423885392069726, Ua=0.12423885392069726, err=0.0 xmax=2.0, ymax=6.3, nx=6, ny=6, npx=6, npy=6 maxerr=0.02680547135252298, avgerr=0.006362785469262094 fem_laplace2_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=2.0, ymin=0.0, ymax=6.3 nx=8, ny=8 x grid and analytic solution at ymin i=0, Ua(0.0)=0.0 i=1, Ua(0.2857142857142857)=0.0 i=2, Ua(0.5714285714285714)=0.0 i=3, Ua(0.8571428571428571)=0.0 i=4, Ua(1.1428571428571428)=0.0 i=5, Ua(1.4285714285714284)=0.0 i=6, Ua(1.7142857142857142)=0.0 i=7, Ua(2.0)=0.0 y grid and analytic solution at xmin ii=0, Ua(0.0)=0.0 ii=1, Ua(0.9)=0.7833269096274834 ii=2, Ua(1.8)=0.9738476308781951 ii=3, Ua(2.7)=0.4273798802338298 ii=4, Ua(3.6)=-0.44252044329485246 ii=5, Ua(4.5)=-0.977530117665097 ii=6, Ua(5.4)=-0.7727644875559871 ii=7, Ua(6.3)=0.016813900484349713 calling gauleg xmin=0.0, xmax=2.0, npx=8 xx[1]=0.039710143502463824, xx[2]=0.20333352258637316, wx[1]=0.10122853629036972, wx[2]=0.22238103445337445 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])=-117.30956371692378 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above writing fem_laplace2_la.dat finished writing fem_laplace2_la.dat check solution nu against PDE Uxx + Uyy = 0 nu maxerr=0.023511490807537106, rmserr=0.009913015134251111, avgerr=0.008199744556431096 check solution against PDE Uxx + Uyy = 0 maxerr=0.023511490795144717, rmserr=0.009913015131486652, avgerr=0.00819974455493524 ug computed Galerkin, Ua analytic, error ug[0,0]=-3.791889143369773E-14, Ua=0.0, err=-3.791889143369773E-14 ug[0,1]=0.783326909627481, Ua=0.7833269096274834, err=-2.4424906541753444E-15 ug[0,2]=0.9738476308782007, Ua=0.9738476308781951, err=5.551115123125783E-15 ug[0,3]=0.4273798802338334, Ua=0.4273798802338298, err=3.608224830031759E-15 ug[0,4]=-0.44252044329485285, Ua=-0.44252044329485246, err=-3.885780586188048E-16 ug[0,5]=-0.9775301176650975, Ua=-0.977530117665097, err=-4.440892098500626E-16 ug[0,6]=-0.7727644875559875, Ua=-0.7727644875559871, err=-3.3306690738754696E-16 ug[0,7]=0.016813900484349713, Ua=0.016813900484349713, err=0.0 ug[1,0]=2.0898467648368155E-15, Ua=0.0, err=2.0898467648368155E-15 ug[1,1]=1.0424667531971716, Ua=1.04238267323003, err=8.40799671415482E-5 ug[1,2]=1.2961750284911713, Ua=1.2959109208648187, err=2.641076263525388E-4 ug[1,3]=0.5683498016532171, Ua=0.5687196195707449, err=-3.698179175277705E-4 ug[1,4]=-0.5884826100162258, Ua=-0.5888673515122685, err=3.8474149604272867E-4 ug[1,5]=-1.3011100612612587, Ua=-1.3008112509490877, err=-2.988103121710495E-4 ug[1,6]=-1.0283920633050188, Ua=-1.028327129344903, err=-6.493396011575392E-5 ug[1,7]=0.022374462461190067, Ua=0.022374462461190067, err=0.0 ug[2,0]=-6.836942121530505E-16, Ua=0.0, err=-6.836942121530505E-16 ug[2,1]=1.3872333091594646, Ua=1.3871113376749764, err=1.2197148448822581E-4 ug[2,2]=1.7249285750581225, Ua=1.7244844692000418, err=4.441058580806345E-4 ug[2,3]=0.756207228552223, Ua=0.7568021346904068, err=-5.949061381838039E-4 ug[2,4]=-0.7829926900076942, Ua=-0.7836129673358919, err=6.202773281976937E-4 ug[2,5]=-1.7315090150052042, Ua=-1.731005398214697, err=-5.036167905072553E-4 ug[2,6]=-1.3684965768672728, Ua=-1.368407453985281, err=-8.912288199169893E-5 ug[2,7]=0.029773970108433478, Ua=0.029773970108433478, err=0.0 ug[3,0]=1.503672800648855E-14, Ua=0.0, err=1.503672800648855E-14 ug[3,1]=1.8460161753312696, Ua=1.8458459762616009, err=1.7019906966875276E-4 ug[3,2]=2.2953979979568007, Ua=2.2947925174730144, err=6.054804837862804E-4 ug[3,3]=1.0062671625286705, Ua=1.0070858316867166, err=-8.186691580460703E-4 ug[3,4]=-1.0419097662806598, Ua=-1.0427633337117832, err=8.535674311234143E-4 ug[3,5]=-2.304156874529271, Ua=-2.3034699972515043, err=-6.868772777668397E-4 ug[3,6]=-1.8210817346098822, Ua=-1.8209564900960868, err=-1.2524451379536394E-4 ug[3,7]=0.039620585189746184, Ua=0.03962058518972523, err=2.095545958979983E-14 ug[4,0]=7.727086295484888E-15, Ua=0.0, err=7.727086295484888E-15 ug[4,1]=2.4565375436935004, Ua=2.456289755220424, err=2.4778847307649343E-4 ug[4,2]=3.054468301285689, Ua=3.0537083936122515, err=7.599076734372545E-4 ug[4,3]=1.339074072817417, Ua=1.3401414001019227, err=-0.001067327284505648 ug[4,4]=-1.386506687529165, Ua=-1.3876178872211313, err=0.0011111996919663802 ug[4,5]=-3.0661164452284257, Ua=-3.0652556217965907, err=-8.608234318350227E-4 ug[4,6]=-2.4233609876863653, Ua=-2.4231690123917775, err=-1.9197529458780949E-4 ug[4,7]=0.05272359598197015, Ua=0.052723595981969185, err=9.645062526431047E-16 ug[5,0]=0.0, Ua=0.0, err=0.0 ug[5,1]=3.26895989234316, Ua=3.268614737736783, err=3.451546063768518E-4 ug[5,2]=4.064472784699336, Ua=4.0636070068271755, err=8.65777872160578E-4 ug[5,3]=1.7820559134353438, Ua=1.7833425074197973, err=-0.0012865939844535212 ug[5,4]=-1.8451839384825652, Ua=-1.8465200479212804, err=0.001336109438715205 ug[5,5]=-4.079950679844374, Ua=-4.078973044218783, err=-9.776356255910557E-4 ug[5,6]=-3.2248237536850355, Ua=-3.224540561266186, err=-2.8319241884933177E-4 ug[5,7]=0.07015993226649248, Ua=0.07015993226649248, err=0.0 ug[6,0]=-2.546114794209569E-15, Ua=0.0, err=-2.546114794209569E-15 ug[6,1]=4.349962870125676, Ua=4.349585500262508, err=3.773698631679423E-4 ug[6,2]=5.408260162474552, Ua=5.40749140961744, err=7.687528571125313E-4 ug[6,3]=2.371886890238343, Ua=2.3731156268498657, err=-0.0012287366115226739 ug[6,4]=-2.4559151374607615, Ua=-2.4571867505999134, err=0.001271613139151917 ug[6,5]=-5.4288028649303275, Ua=-5.427939183000884, err=-8.636819294434162E-4 ug[6,6]=-4.2912602090971514, Ua=-4.290935456040638, err=-3.2475305651313846E-4 ug[6,7]=0.09336267763910144, Ua=0.09336267763910144, err=0.0 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=5.788046479039455, Ua=5.788046479039455, err=0.0 ug[7,2]=7.1958147763696925, Ua=7.1958147763696925, err=0.0 ug[7,3]=3.157933910602031, Ua=3.157933910602031, err=0.0 ug[7,4]=-3.2698083804293248, Ua=-3.2698083804293248, err=0.0 ug[7,5]=-7.223024877821682, Ua=-7.223024877821682, err=0.0 ug[7,6]=-5.710000149812585, Ua=-5.710000149812585, err=0.0 ug[7,7]=0.12423885392069726, Ua=0.12423885392069726, err=0.0 xmax=2.0, ymax=6.3, nx=8, ny=8, npx=8, npy=8 maxerr=0.001336109438715205, avgerr=3.3232692105554507E-4 fem_laplace2_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=2.0, 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(0.2222222222222222)=0.0 i=2, Ua(0.4444444444444444)=0.0 i=3, Ua(0.6666666666666666)=0.0 i=4, Ua(0.8888888888888888)=0.0 i=5, Ua(1.1111111111111112)=0.0 i=6, Ua(1.3333333333333333)=0.0 i=7, Ua(1.5555555555555554)=0.0 i=8, Ua(1.7777777777777777)=0.0 i=9, Ua(2.0)=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=2.0, npx=10 xx[1]=0.026093471482828368, xx[2]=0.13493663331101546, wx[1]=0.06667134430868286, wx[2]=0.14945134915058053 calling gauleg ymin=0.0, ymax=6.3, npy=10 yy[1]=0.08219443517090941, yy[2]=0.42505039492969887, wy[1]=0.210014734572351, wy[2]=0.4707717498243287 galk(xx[2],yy[2])=-476.69887305742844 galf(xx[2],yy[2])=0.0 compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above writing fem_laplace2_la.dat finished writing fem_laplace2_la.dat check solution nu against PDE Uxx + Uyy = 0 nu maxerr=0.0010717739021490194, rmserr=2.669959308197607E-4, avgerr=1.733086273474495E-4 check solution against PDE Uxx + Uyy = 0 maxerr=0.0010717761643253458, rmserr=2.669958639814625E-4, avgerr=1.733083785039542E-4 ug computed Galerkin, Ua analytic, error ug[0,0]=1.0556333630222473E-13, Ua=0.0, err=1.0556333630222473E-13 ug[0,1]=0.6442176872377019, Ua=0.644217687237691, err=1.0880185641326534E-14 ug[0,2]=0.9854497299884545, Ua=0.9854497299884601, err=-5.662137425588298E-15 ug[0,3]=0.8632093666488321, Ua=0.8632093666488739, err=-4.18554080283684E-14 ug[0,4]=0.33498815015591227, Ua=0.3349881501559051, err=7.16093850883226E-15 ug[0,5]=-0.3507832276896221, Ua=-0.35078322768961984, err=-2.275957200481571E-15 ug[0,6]=-0.871575772413601, Ua=-0.8715757724135877, err=-1.3211653993039363E-14 ug[0,7]=-0.9824526126243305, Ua=-0.9824526126243326, err=2.1094237467877974E-15 ug[0,8]=-0.6312666378723338, Ua=-0.6312666378723216, err=-1.2212453270876722E-14 ug[0,9]=0.016813900484349713, Ua=0.016813900484349713, err=0.0 ug[1,0]=3.4470619910398607E-13, Ua=0.0, err=3.4470619910398607E-13 ug[1,1]=0.8045212419724049, Ua=0.8045305300976698, err=-9.288125264905744E-6 ug[1,2]=1.2306777100576098, Ua=1.2306777807541014, err=-7.069649154978208E-8 ug[1,3]=1.0780207318685033, Ua=1.0780180412511045, err=2.690617398881656E-6 ug[1,4]=0.4183408496185322, Ua=0.4183495724511678, err=-8.722832635588151E-6 ug[1,5]=-0.4380660253752997, Ua=-0.4380752371649413, err=9.211789641583312E-6 ug[1,6]=-1.0884700102062457, Ua=-1.0884664176279766, err=-3.5925782690959807E-6 ug[1,7]=-1.2269339448786718, Ua=-1.2269348341236455, err=8.89244973656389E-7 ug[1,8]=-0.7883473710043486, Ua=-0.7883566267453433, err=9.255740994751349E-6 ug[1,9]=0.020998020603386975, Ua=0.020998020603386975, err=0.0 ug[2,0]=-2.1789723652623643E-14, Ua=0.0, err=-2.1789723652623643E-14 ug[2,1]=1.0047254602753464, Ua=1.0047370425897988, err=-1.158231445241853E-5 ug[2,2]=1.5369291304675428, Ua=1.5369305546002598, err=-1.4241327170871898E-6 ug[2,3]=1.3462851148437354, Ua=1.3462816115798506, err=3.503263884763186E-6 ug[2,4]=0.5224426122018644, Ua=0.5224553904029782, err=-1.277820111378336E-5 ug[2,5]=-0.5470762036325075, Ua=-0.5470897644710806, err=1.356083857306789E-5 ug[2,6]=-1.3593349600010682, Ua=-1.3593300546010112, err=-4.9054000570425416E-6 ug[2,7]=-1.532253441601812, Ua=-1.5322561799340813, err=2.738332269158761E-6 ug[2,8]=-0.9845268144914276, Ua=-0.9845382816809033, err=1.1467189475644624E-5 ug[2,9]=0.026223354281776124, Ua=0.026223354281813844, err=-3.7719827261639693E-14 ug[3,0]=5.178595997159446E-16, Ua=0.0, err=5.178595997159446E-16 ug[3,1]=1.2547509829311103, Ua=1.2547647192823652, err=-1.373635125490047E-5 ug[3,2]=1.9193914292240888, Ua=1.9193939848466626, err=-2.5556225737854987E-6 ug[3,3]=1.6813065271498306, Ua=1.6813022679792584, err=4.259170572229465E-6 ug[3,4]=0.652451493913269, Ua=0.6524678234085916, err=-1.6329495322597865E-5 ug[3,5]=-0.6832150711938167, Ua=-0.6832324336021056, err=1.7362408288867925E-5 ug[3,6]=-1.6976038945480032, Ua=-1.6975978012884676, err=-6.093259535600026E-6 ug[3,7]=-1.9135521008299041, Ua=-1.9135563973315153, err=4.296501611156245E-6 ug[3,8]=-1.2295259673093397, Ua=-1.2295395195660557, err=1.3552256715954059E-5 ug[3,9]=0.03274900633624391, Ua=0.03274900633627364, err=-2.9726221484338566E-14 ug[4,0]=6.64085193847282E-15, Ua=0.0, err=6.64085193847282E-15 ug[4,1]=1.566994022790422, Ua=1.5670115005389949, err=-1.747774857285833E-5 ug[4,2]=2.3970297951671378, Ua=2.3970330071443864, err=-3.211977248618325E-6 ug[4,3]=2.099697943096294, Ua=2.09969243581586, err=5.507280433914019E-6 ug[4,4]=0.814813307415725, Ua=0.8148337033238088, err=-2.0395908083781222E-5 ug[4,5]=-0.8532323653778066, Ua=-0.8532540519692565, err=2.168659144996532E-5 ug[4,6]=-2.120050917623393, Ua=-2.120043094158845, err=-7.823464547751513E-6 ug[4,7]=-2.389737340988895, Ua=-2.389742742578396, err=5.401589501019544E-6 ug[4,8]=-1.535491776854849, Ua=-1.5355090384029402, err=1.7261548091118684E-5 ug[4,9]=0.040898559523984246, Ua=0.04089855952398425, err=-6.938893903907228E-18 ug[5,0]=1.105497868455555E-18, Ua=0.0, err=1.105497868455555E-18 ug[5,1]=1.956936673236299, Ua=1.9569605401607528, err=-2.386692445388583E-5 ug[5,2]=2.9935288554953052, Ua=2.9935319599319685, err=-3.1044366632926312E-6 ug[5,3]=2.622206054684143, Ua=2.6221985237200243, err=7.530964118540595E-6 ug[5,4]=1.0175786907553124, Ua=1.017604148820391, err=-2.545806507869841E-5 ug[5,5]=-1.0655583289355692, Ua=-1.0655853577729089, err=2.7028837339626577E-5 ug[5,6]=-2.6476238403105494, Ua=-2.647613420375101, err=-1.0419935448258144E-5 ug[5,7]=-2.9844217319891286, Ua=-2.984427521274009, err=5.789284880375334E-6 ug[5,8]=-1.9175950521464442, Ua=-1.9176187259513726, err=2.367380492840354E-5 ug[5,9]=0.05107611980532635, Ua=0.05107611980532572, err=6.314393452555578E-16 ug[6,0]=0.0, Ua=0.0, err=0.0 ug[6,1]=2.4439143745545113, Ua=2.443947957260677, err=-3.358270616571346E-5 ug[6,2]=3.7384672894411035, Ua=3.7384690024814273, err=-1.7130403238141412E-6 ug[6,3]=3.274740082283756, Ua=3.2747296606456326, err=1.0421638123148114E-5 ug[6,4]=1.270802206547441, Ua=1.2708337903457647, err=-3.158379832379765E-5 ug[6,5]=-1.330721632912063, Ua=-1.3307550688794498, err=3.3435967386807874E-5 ug[6,6]=-3.3064829640850415, Ua=-3.3064690255891196, err=-1.3938495921905769E-5 ug[6,7]=-3.727094039565284, Ua=-3.727098934560539, err=4.894995254911549E-6 ug[6,8]=-2.3947824902345896, Ua=-2.394815977080818, err=3.348684622839215E-5 ug[6,9]=0.06378635445188112, Ua=0.06378635445187543, err=5.689893001203927E-15 ug[7,0]=0.0, Ua=0.0, err=0.0 ug[7,1]=3.0520762671624326, Ua=3.0521216423239674, err=-4.53751615347997E-5 ug[7,2]=4.66878427265012, Ua=4.668782785546777, err=1.4871033426899771E-6 ug[7,3]=4.089656057388765, Ua=4.089642432983561, err=1.3624405204026857E-5 ug[7,4]=1.5870418869638163, Ua=1.587079341762429, err=-3.7454798612612805E-5 ug[7,5]=-1.661872477519586, Ua=-1.6619119626883563, err=3.9485168770170276E-5 ug[7,6]=-4.129297712086834, Ua=-4.1292801029960655, err=-1.7609090768644364E-5 ug[7,7]=-4.65458129021727, Ua=-4.654583289083304, err=1.998866033581237E-6 ug[7,8]=-2.9907177709063197, Ua=-2.990763224444538, err=4.5453538218165335E-5 ug[7,9]=0.07965951661496504, Ua=0.07965951661496504, err=0.0 ug[8,0]=0.0, Ua=0.0, err=0.0 ug[8,1]=3.8115890184029215, Ua=3.811638661071844, err=-4.964266892226732E-5 ug[8,2]=5.830609620034591, Ua=5.830604101344616, err=5.518689974337576E-6 ug[8,3]=5.107359534885881, Ua=5.1073453270528075, err=1.4207833073598408E-5 ug[8,4]=1.9819857420101692, Ua=1.9820222409759438, err=-3.649896577462286E-5 ug[8,5]=-2.075438611486658, Ua=-2.07547687498372, err=3.8263497061929996E-5 ug[8,6]=-5.156864560255435, Ua=-5.156846786417787, err=-1.7773837647894197E-5 ug[8,7]=-5.812873591680332, Ua=-5.812871076245814, err=-2.5154345184574822E-6 ug[8,8]=-3.734961380895425, Ua=-3.7350112702993856, err=4.988940396044583E-5 ug[8,9]=0.09948269722981981, Ua=0.09948269722981981, err=0.0 ug[9,0]=0.0, Ua=0.0, err=0.0 ug[9,1]=4.760160630922659, Ua=4.760160630922659, err=0.0 ug[9,2]=7.2815433375607945, Ua=7.2815433375607945, err=0.0 ug[9,3]=6.378302435290926, Ua=6.378302435290926, err=0.0 ug[9,4]=2.475246233978987, Ua=2.475246233978987, err=0.0 ug[9,5]=-2.5919569479625646, Ua=-2.5919569479625646, err=0.0 ug[9,6]=-6.440122276832813, Ua=-6.440122276832813, err=0.0 ug[9,7]=-7.2593974692221765, Ua=-7.2593974692221765, err=0.0 ug[9,8]=-4.664464600621924, Ua=-4.664464600621924, err=0.0 ug[9,9]=0.12423885392069726, Ua=0.12423885392069726, err=0.0 xmax=2.0, ymax=6.3, nx=10, ny=10, npx=10, npy=10 maxerr=4.988940396044583E-5, avgerr=9.893606767232746E-6