laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=5, ny=4 x grid and analytic solution at ymin i=0, Ua(1.0)=1.8221188003905089 i=1, Ua(1.5)=2.0137527074704766 i=2, Ua(2.0)=2.225540928492468 i=3, Ua(2.5)=2.45960311115695 i=4, Ua(3.0)=2.7182818284590455 y grid and analytic solution at xmin ii=0, Ua(1.0)=1.8221188003905089 ii=1, Ua(1.3333333333333333)=2.0820090840784555 ii=2, Ua(1.6666666666666665)=2.3789677299066345 ii=3, Ua(2.0)=2.7182818284590455 solution at i=0,x=1.0, ii=0,y=1.0 is1.8221188003905089 solution at i=0,x=1.0, ii=1,y=1.3333333333333333 is2.0820090840784555 solution at i=0,x=1.0, ii=2,y=1.6666666666666665 is2.3789677299066345 solution at i=0,x=1.0, ii=3,y=2.0 is2.7182818284590455 solution at i=1,x=1.5, ii=0,y=1.0 is2.0137527074704766 solution at i=1,x=1.5, ii=1,y=1.3333333333333333 is2.3009758908928246 solution at i=1,x=1.5, ii=2,y=1.6666666666666665 is2.6291659501332543 solution at i=1,x=1.5, ii=3,y=2.0 is3.0041660239464334 solution at i=2,x=2.0, ii=0,y=1.0 is2.225540928492468 solution at i=2,x=2.0, ii=1,y=1.3333333333333333 is2.5429716378079545 solution at i=2,x=2.0, ii=2,y=1.6666666666666665 is2.9056777468820014 solution at i=2,x=2.0, ii=3,y=2.0 is3.3201169227365472 solution at i=3,x=2.5, ii=0,y=1.0 is2.45960311115695 solution at i=3,x=2.5, ii=1,y=1.3333333333333333 is2.81041829959655 solution at i=3,x=2.5, ii=2,y=1.6666666666666665 is3.21127054315356 solution at i=3,x=2.5, ii=3,y=2.0 is3.6692966676192444 solution at i=4,x=3.0, ii=0,y=1.0 is2.7182818284590455 solution at i=4,x=3.0, ii=1,y=1.3333333333333333 is3.10599257234172 solution at i=4,x=3.0, ii=2,y=1.6666666666666665 is3.549002814366304 solution at i=4,x=3.0, ii=3,y=2.0 is4.0551999668446745 boundary i=0,x=1.0, ii=0,y=1.0 is 1.8221188003905089 boundary i=0,x=1.0, ii=3,y=2.0 is 2.7182818284590455 boundary i=1,x=1.5, ii=0,y=1.0 is 2.0137527074704766 boundary i=1,x=1.5, ii=3,y=2.0 is 3.0041660239464334 boundary i=2,x=2.0, ii=0,y=1.0 is 2.225540928492468 boundary i=2,x=2.0, ii=3,y=2.0 is 3.3201169227365472 boundary i=3,x=2.5, ii=0,y=1.0 is 2.45960311115695 boundary i=3,x=2.5, ii=3,y=2.0 is 3.6692966676192444 boundary i=4,x=3.0, ii=0,y=1.0 is 2.7182818284590455 boundary i=4,x=3.0, ii=3,y=2.0 is 4.0551999668446745 boundary i=0,x=1.0, ii=0,y=1.0 is 1.8221188003905089 boundary i=4,x=3.0, ii=0,y=1.0 is 2.7182818284590455 boundary i=0,x=1.0, ii=1,y=1.3333333333333333 is 2.0820090840784555 boundary i=4,x=3.0, ii=1,y=1.3333333333333333 is 3.10599257234172 boundary i=0,x=1.0, ii=2,y=1.6666666666666665 is 2.3789677299066345 boundary i=4,x=3.0, ii=2,y=1.6666666666666665 is 3.549002814366304 boundary i=0,x=1.0, ii=3,y=2.0 is 2.7182818284590455 boundary i=4,x=3.0, ii=3,y=2.0 is 4.0551999668446745 calling gauleg xmin=1.0, xmax=3.0, npx=3 calling gauleg ymin=1.0, ymax=2.0, npy=3 compute stiffness matrix Legendre integration=1.2555156309711404, at i=1, j=0, ii=1, jj=0 Legendre integration=-0.42782205793856676, at i=1, j=0, ii=1, jj=1 Legendre integration=1.4360847550786264, at i=1, j=0, ii=1, jj=2 Legendre integration=-0.4491149266884977, at i=1, j=0, ii=1, jj=3 Legendre integration=-0.456438607998677, at i=1, j=0, ii=2, jj=0 Legendre integration=1.4360847550786264, at i=1, j=0, ii=2, jj=1 Legendre integration=-0.4457983666090067, at i=1, j=0, ii=2, jj=2 Legendre integration=1.2408682683507808, at i=1, j=0, ii=2, jj=3 Legendre integration=2.0988371404408226, at i=1, j=1, ii=1, jj=0 Legendre integration=-10.801860824281167, at i=1, j=1, ii=1, jj=1 Legendre integration=4.583944176716304, at i=1, j=1, ii=1, jj=2 Legendre integration=-0.33687193322678793, at i=1, j=1, ii=1, jj=3 Legendre integration=-0.3627425996731383, at i=1, j=1, ii=2, jj=0 Legendre integration=4.583944176716304, at i=1, j=1, ii=2, jj=1 Legendre integration=-10.86536155101312, at i=1, j=1, ii=2, jj=2 Legendre integration=2.047095807548121, at i=1, j=1, ii=2, jj=3 Legendre integration=-0.8486802496646296, at i=1, j=2, ii=1, jj=0 Legendre integration=8.45196821073785, at i=1, j=2, ii=1, jj=1 Legendre integration=-2.7375632889390413, at i=1, j=2, ii=1, jj=2 Legendre integration=-0.031378268051565635, at i=1, j=2, ii=1, jj=3 Legendre integration=-0.015399327011172179, at i=1, j=2, ii=2, jj=0 Legendre integration=-2.7375632889390418, at i=1, j=2, ii=2, jj=1 Legendre integration=8.491189247836997, at i=1, j=2, ii=2, jj=2 Legendre integration=-0.8167223675838433, at i=1, j=2, ii=2, jj=3 Legendre integration=0.7146542238719721, at i=1, j=3, ii=1, jj=0 Legendre integration=-5.042637943119663, at i=1, j=3, ii=1, jj=1 Legendre integration=1.856200483715795, at i=1, j=3, ii=1, jj=2 Legendre integration=-0.05870789852836053, at i=1, j=3, ii=1, jj=3 Legendre integration=-0.0693605258886226, at i=1, j=3, ii=2, jj=0 Legendre integration=1.8562004837157948, at i=1, j=3, ii=2, jj=1 Legendre integration=-5.068785301185762, at i=1, j=3, ii=2, jj=2 Legendre integration=0.6933489691514477, at i=1, j=3, ii=2, jj=3 Legendre integration=0.2199356049722736, at i=1, j=4, ii=1, jj=0 Legendre integration=0.38183795256960634, at i=1, j=4, ii=1, jj=1 Legendre integration=0.15269688939090106, at i=1, j=4, ii=1, jj=2 Legendre integration=-0.09741816150793761, at i=1, j=4, ii=1, jj=3 Legendre integration=-0.09808395071795384, at i=1, j=4, ii=2, jj=0 Legendre integration=0.1526968893909011, at i=1, j=4, ii=2, jj=1 Legendre integration=0.3802037426904759, at i=1, j=4, ii=2, jj=2 Legendre integration=0.21860402655224095, at i=1, j=4, ii=2, jj=3 Legendre integration=-0.6707183586869453, at i=2, j=0, ii=1, jj=0 Legendre integration=-0.08012948288831215, at i=2, j=0, ii=1, jj=1 Legendre integration=-0.7003681551915886, at i=2, j=0, ii=1, jj=2 Legendre integration=0.2525918118561531, at i=2, j=0, ii=1, jj=3 Legendre integration=0.2560872052087386, at i=2, j=0, ii=2, jj=0 Legendre integration=-0.7003681551915887, at i=2, j=0, ii=2, jj=1 Legendre integration=-0.07154988102287523, at i=2, j=0, ii=2, jj=2 Legendre integration=-0.6637275719817738, at i=2, j=0, ii=2, jj=3 Legendre integration=-0.8486802496646279, at i=2, j=1, ii=1, jj=0 Legendre integration=8.451968210737856, at i=2, j=1, ii=1, jj=1 Legendre integration=-2.7375632889390404, at i=2, j=1, ii=1, jj=2 Legendre integration=-0.03137826805156649, at i=2, j=1, ii=1, jj=3 Legendre integration=-0.015399327011173136, at i=2, j=1, ii=2, jj=0 Legendre integration=-2.737563288939041, at i=2, j=1, ii=2, jj=1 Legendre integration=8.491189247837006, at i=2, j=1, ii=2, jj=2 Legendre integration=-0.816722367583841, at i=2, j=1, ii=2, jj=3 Legendre integration=4.326105178024977, at i=2, j=2, ii=1, jj=0 Legendre integration=-19.54421724106938, at i=2, j=2, ii=1, jj=1 Legendre integration=8.85953997782051, at i=2, j=2, ii=1, jj=2 Legendre integration=-0.8059937327975519, at i=2, j=2, ii=1, jj=3 Legendre integration=-0.8556425853159153, at i=2, j=2, ii=2, jj=0 Legendre integration=8.85953997782051, at i=2, j=2, ii=2, jj=1 Legendre integration=-19.666082606341728, at i=2, j=2, ii=2, jj=2 Legendre integration=4.2268074729882485, at i=2, j=2, ii=2, jj=3 Legendre integration=-0.8366157552846233, at i=2, j=3, ii=1, jj=0 Legendre integration=8.499945618621128, at i=2, j=3, ii=1, jj=1 Legendre integration=-2.7350381622083413, at i=2, j=3, ii=1, jj=2 Legendre integration=-0.037831369696685074, at i=2, j=3, ii=1, jj=3 Legendre integration=-0.021852428656292056, at i=2, j=3, ii=2, jj=0 Legendre integration=-2.7350381622083404, at i=2, j=3, ii=2, jj=1 Legendre integration=8.539166655720278, at i=2, j=3, ii=2, jj=2 Legendre integration=-0.8046578732038367, at i=2, j=3, ii=2, jj=3 Legendre integration=-0.6654401423956936, at i=2, j=4, ii=1, jj=0 Legendre integration=-0.05913936693938113, at i=2, j=4, ii=1, jj=1 Legendre integration=-0.6992634122469079, at i=2, j=4, ii=1, jj=2 Legendre integration=0.24976857988641366, at i=2, j=4, ii=1, jj=3 Legendre integration=0.2532639732389993, at i=2, j=4, ii=2, jj=0 Legendre integration=-0.6992634122469079, at i=2, j=4, ii=2, jj=1 Legendre integration=-0.05055976507394411, at i=2, j=4, ii=2, jj=2 Legendre integration=-0.6584493556905219, at i=2, j=4, ii=2, jj=3 Legendre integration=0.22295172856727455, at i=3, j=0, ii=1, jj=0 Legendre integration=0.39383230454042417, at i=3, j=0, ii=1, jj=1 Legendre integration=0.15332817107357566, at i=3, j=0, ii=1, jj=2 Legendre integration=-0.09903143691921718, at i=3, j=0, ii=1, jj=3 Legendre integration=-0.0996972261292334, at i=3, j=0, ii=2, jj=0 Legendre integration=0.15332817107357566, at i=3, j=0, ii=2, jj=1 Legendre integration=0.3921980946612936, at i=3, j=0, ii=2, jj=2 Legendre integration=0.22162015014724196, at i=3, j=0, ii=2, jj=3 Legendre integration=0.7146542238719723, at i=3, j=1, ii=1, jj=0 Legendre integration=-5.0426379431196615, at i=3, j=1, ii=1, jj=1 Legendre integration=1.8562004837157953, at i=3, j=1, ii=1, jj=2 Legendre integration=-0.05870789852836062, at i=3, j=1, ii=1, jj=3 Legendre integration=-0.06936052588862279, at i=3, j=1, ii=2, jj=0 Legendre integration=1.8562004837157957, at i=3, j=1, ii=2, jj=1 Legendre integration=-5.068785301185761, at i=3, j=1, ii=2, jj=2 Legendre integration=0.693348969151448, at i=3, j=1, ii=2, jj=3 Legendre integration=-0.836615755284625, at i=3, j=2, ii=1, jj=0 Legendre integration=8.49994561862112, at i=3, j=2, ii=1, jj=1 Legendre integration=-2.7350381622083417, at i=3, j=2, ii=1, jj=2 Legendre integration=-0.0378313696966841, at i=3, j=2, ii=1, jj=3 Legendre integration=-0.02185242865629089, at i=3, j=2, ii=2, jj=0 Legendre integration=-2.7350381622083417, at i=3, j=2, ii=2, jj=1 Legendre integration=8.53916665572027, at i=3, j=2, ii=2, jj=2 Legendre integration=-0.8046578732038386, at i=3, j=2, ii=2, jj=3 Legendre integration=2.0712611532865264, at i=3, j=3, ii=1, jj=0 Legendre integration=-10.9115234708715, at i=3, j=3, ii=1, jj=1 Legendre integration=4.578172458474706, at i=3, j=3, ii=1, jj=2 Legendre integration=-0.32212198660937386, at i=3, j=3, ii=1, jj=3 Legendre integration=-0.34799265305572424, at i=3, j=3, ii=2, jj=0 Legendre integration=4.578172458474704, at i=3, j=3, ii=2, jj=1 Legendre integration=-10.975024197603453, at i=3, j=3, ii=2, jj=2 Legendre integration=2.0195198203938247, at i=3, j=3, ii=2, jj=3 Legendre integration=1.2464672601861375, at i=3, j=4, ii=1, jj=0 Legendre integration=-0.46380511385102025, at i=3, j=4, ii=1, jj=1 Legendre integration=1.4341909100306027, at i=3, j=4, ii=1, jj=2 Legendre integration=-0.4442751004546588, at i=3, j=4, ii=1, jj=3 Legendre integration=-0.45159878176483836, at i=3, j=4, ii=2, jj=0 Legendre integration=1.4341909100306023, at i=3, j=4, ii=2, jj=1 Legendre integration=-0.4817814225214604, at i=3, j=4, ii=2, jj=2 Legendre integration=1.2318198975657775, at i=3, j=4, ii=2, jj=3 Legendre integration=0.811779516984777, f at i=1, ii=1 Legendre integration=0.592520070331291, f at i=1, ii=2 Legendre integration=0.520515969195476, f at i=2, ii=1 Legendre integration=0.486295514299371, f at i=2, ii=2 Legendre integration=0.7266016481835789, f at i=3, ii=1 Legendre integration=0.3870504479135357, f at i=3, ii=2 k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[0,0]=1.8221188003905087, U=1.8221188003905089, err=-2.220446049250313E-16 u[0,1]=2.0820090840784555, U=2.0820090840784555, err=0.0 u[0,2]=2.378967729906635, U=2.3789677299066345, err=4.440892098500626E-16 u[0,3]=2.7182818284590455, U=2.7182818284590455, err=0.0 u[1,0]=2.0137527074704766, U=2.0137527074704766, err=0.0 u[1,1]=2.300967457478128, U=2.3009758908928246, err=-8.433414696806807E-6 u[1,2]=2.6291536572590837, U=2.6291659501332543, err=-1.2292874170594104E-5 u[1,3]=3.0041660239464334, U=3.0041660239464334, err=0.0 u[2,0]=2.2255409284924674, U=2.225540928492468, err=-4.440892098500626E-16 u[2,1]=2.542958954879346, U=2.5429716378079545, err=-1.2682928608676036E-5 u[2,2]=2.9056607563129853, U=2.9056777468820014, err=-1.6990569016162027E-5 u[2,3]=3.3201169227365472, U=3.3201169227365472, err=0.0 u[3,0]=2.4596031111569494, U=2.45960311115695, err=-4.440892098500626E-16 u[3,1]=2.8104059015933895, U=2.81041829959655, err=-1.2398003160551951E-5 u[3,2]=3.211252777287794, U=3.21127054315356, err=-1.7765865766072864E-5 u[3,3]=3.6692966676192444, U=3.6692966676192444, err=0.0 u[4,0]=2.7182818284590455, U=2.7182818284590455, err=0.0 u[4,1]=3.10599257234172, U=3.10599257234172, err=0.0 u[4,2]=3.549002814366304, U=3.549002814366304, err=0.0 u[4,3]=4.0551999668446745, U=4.0551999668446745, err=0.0 nx=5, ny=4, np=3 maxerr=1.7765865766072864E-5, avgerr=4.028182771020905E-6 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=5, ny=4 calling gauleg xmin=1.0, xmax=3.0, npx=4 calling gauleg ymin=1.0, ymax=2.0, npy=4 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=2.3009658046089387, U=2.3009758908928246, err=-1.008628388587951E-5 u[1,2]=2.629154479614279, U=2.6291659501332543, err=-1.1470518975098543E-5 u[2,1]=2.5429587618301066, U=2.5429716378079545, err=-1.2875977847937037E-5 u[2,2]=2.9056636022816322, U=2.9056777468820014, err=-1.4144600369192517E-5 u[3,1]=2.8104060419541934, U=2.81041829959655, err=-1.2257642356683363E-5 u[3,2]=3.211256550990826, U=3.21127054315356, err=-1.3992162734233204E-5 nx=5, ny=4, np=4 maxerr=1.4144600369192517E-5, avgerr=3.741359308673253E-6 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=6, ny=6 calling gauleg xmin=1.0, xmax=3.0, npx=3 calling gauleg ymin=1.0, ymax=2.0, npy=3 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u redundant row (singular) 14 redundant row (singular) 15 redundant row (singular) 9 redundant row (singular) 26 redundant row (singular) 16 redundant row (singular) 20 redundant row (singular) 19 u computed Galerkin, U analytic, error u[1,1]=-1920.9506310365612, U=2.1382762204968184, err=-1923.088907257058 u[1,2]=-1529.1646954046894, U=2.3163669767810915, err=-1531.4810623814706 u[1,3]=1532.2655197694457, U=2.5092903899362975, err=1529.7562293795095 u[1,4]=1922.3831926866528, U=2.7182818284590455, err=1919.6649108581937 u[2,1]=43.69269795717844, U=2.316366976781092, err=41.37633098039735 u[2,2]=55.95127787081854, U=2.5092903899362975, err=53.44198748088224 u[2,3]=-48.29485796716342, U=2.7182818284590455, err=-51.01313979562247 u[2,4]=-34.70246616038979, U=2.9446795510655237, err=-37.647145711455316 u[3,1]=-0.31293799851375625, U=2.5092903899362975, err=-2.822228388450054 u[3,2]=0.0, U=2.7182818284590455, err=-2.7182818284590455 u[3,3]=0.0, U=2.9446795510655237, err=-2.9446795510655237 u[3,4]=0.0, U=3.189933276116185, err=-3.189933276116185 u[4,1]=0.0, U=2.7182818284590455, err=-2.7182818284590455 u[4,2]=0.0, U=2.9446795510655237, err=-2.9446795510655237 u[4,3]=0.0, U=3.189933276116185, err=-3.189933276116185 u[4,4]=0.0, U=3.4556134647626755, err=-3.4556134647626755 nx=6, ny=6, np=3 maxerr=1923.088907257058, avgerr=197.54037069469672 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=6, ny=6 calling gauleg xmin=1.0, xmax=3.0, npx=4 calling gauleg ymin=1.0, ymax=2.0, npy=4 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=2.1382761793201843, U=2.1382762204968184, err=-4.1176634102413345E-8 u[1,2]=2.3163669798769604, U=2.3163669767810915, err=3.095868894575915E-9 u[1,3]=2.5092903911113136, U=2.5092903899362975, err=1.1750160844314905E-9 u[1,4]=2.718281782148552, U=2.7182818284590455, err=-4.6310493662105046E-8 u[2,1]=2.3163669731445475, U=2.316366976781092, err=-3.6365443989438972E-9 u[2,2]=2.5092904254666695, U=2.5092903899362975, err=3.553037197789877E-8 u[2,3]=2.7182818644349385, U=2.7182818284590455, err=3.5975892931361386E-8 u[2,4]=2.9446795481780033, U=2.9446795510655237, err=-2.8875204449718694E-9 u[3,1]=2.509290384611162, U=2.5092903899362975, err=-5.32513544371227E-9 u[3,2]=2.71828186528863, U=2.7182818284590455, err=3.6829584271202975E-8 u[3,3]=2.944679588292227, U=2.9446795510655237, err=3.7226703497594826E-8 u[3,4]=3.189933271405929, U=3.189933276116185, err=-4.710255741002811E-9 u[4,1]=2.718281779593746, U=2.7182818284590455, err=-4.886529936243278E-8 u[4,2]=2.944679558874594, U=2.9446795510655237, err=7.809070279307662E-9 u[4,3]=3.1899332818346875, U=3.189933276116185, err=5.718502560370098E-9 u[4,4]=3.4556134101783478, U=3.4556134647626755, err=-5.458432772442734E-8 nx=6, ny=6, np=4 maxerr=5.458432772442734E-8, avgerr=1.0301590198164629E-8 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=6, ny=6 calling gauleg xmin=1.0, xmax=3.0, npx=5 calling gauleg ymin=1.0, ymax=2.0, npy=5 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=2.138276205941695, U=2.1382762204968184, err=-1.4555123328818809E-8 u[1,2]=2.3163669740424537, U=2.3163669767810915, err=-2.7386377610127965E-9 u[1,3]=2.509290387598097, U=2.5092903899362975, err=-2.338200300044946E-9 u[1,4]=2.718281812979501, U=2.7182818284590455, err=-1.5479544313024007E-8 u[2,1]=2.316366970737315, U=2.316366976781092, err=-6.043777034392406E-9 u[2,2]=2.509290399166062, U=2.5092903899362975, err=9.229764508233984E-9 u[2,3]=2.7182818387068104, U=2.7182818284590455, err=1.0247764858917208E-8 u[2,4]=2.9446795455345818, U=2.9446795510655237, err=-5.530941926679134E-9 u[3,1]=2.5092903842081036, U=2.5092903899362975, err=-5.728193919196656E-9 u[3,2]=2.7182818386627634, U=2.7182818284590455, err=1.020371787063823E-8 u[3,3]=2.9446795623392488, U=2.9446795510655237, err=1.1273725064597784E-8 u[3,4]=3.189933271061523, U=3.189933276116185, err=-5.05466202227467E-9 u[4,1]=2.718281811482373, U=2.7182818284590455, err=-1.6976672512214463E-8 u[4,2]=2.9446795496453237, U=2.9446795510655237, err=-1.4201999576357593E-9 u[4,3]=3.189933275312106, U=3.189933276116185, err=-8.040790255847696E-10 u[4,4]=3.4556134468166615, U=3.4556134647626755, err=-1.7946014008174416E-8 nx=6, ny=6, np=5 maxerr=1.7946014008174416E-8, avgerr=3.765861671883247E-9 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=8, ny=8 calling gauleg xmin=1.0, xmax=3.0, npx=5 calling gauleg ymin=1.0, ymax=2.0, npy=5 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u redundant row (singular) 34 redundant row (singular) 30 redundant row (singular) 37 redundant row (singular) 54 redundant row (singular) 51 redundant row (singular) 20 redundant row (singular) 12 redundant row (singular) 44 redundant row (singular) 49 u computed Galerkin, U analytic, error u[1,1]=448.64487819686246, U=2.042727070266142, err=446.6021511265963 u[1,2]=-267.21877127712565, U=2.162853839040405, err=-269.38162511616605 u[1,3]=-381.7216265633525, U=2.290044909642452, err=-384.011671472995 u[1,4]=397.51028652175916, U=2.4247157128777834, err=395.08557080888136 u[1,5]=282.50673725226704, U=2.5673061098152665, err=279.9394311424518 u[1,6]=-434.7702465178765, U=2.7182818284590455, err=-437.48852834633556 u[2,1]=-1681.2355827113922, U=2.162853839040405, err=-1683.3984365504327 u[2,2]=2159.684918980852, U=2.290044909642452, err=2157.39487407121 u[2,3]=2231.6574688912733, U=2.4247157128777834, err=2229.2327531783953 u[2,4]=-2227.480191071179, U=2.5673061098152665, err=-2230.0474971809945 u[2,5]=-2155.396036027592, U=2.7182818284590455, err=-2158.114317856051 u[2,6]=1682.4772263491216, U=2.878135984906894, err=1679.5990903642146 u[3,1]=-939.436585307182, U=2.290044909642452, err=-941.7266302168244 u[3,2]=1409.080284786754, U=2.4247157128777834, err=1406.6555690738762 u[3,3]=1377.296742460845, U=2.5673061098152665, err=1374.7294363510298 u[3,4]=-1373.047061775816, U=2.7182818284590455, err=-1375.7653436042751 u[3,5]=-1404.9273197725913, U=2.878135984906894, err=-1407.8054557574983 u[3,6]=940.5021182308602, U=3.0473906939634254, err=937.4547275368968 u[4,1]=-954.7848691348488, U=2.4247157128777834, err=-957.2095848477265 u[4,2]=1195.5406515948812, U=2.5673061098152665, err=1192.973345485066 u[4,3]=1263.4426759710773, U=2.7182818284590455, err=1260.7243941426182 u[4,4]=-1243.4693548804328, U=2.878135984906894, err=-1246.3474908653398 u[4,5]=-1176.3171734314162, U=3.0473906939634254, err=-1179.3645641253797 u[4,6]=971.1440329029717, U=3.2265987744687132, err=967.917434128503 u[5,1]=14.537285792408733, U=2.5673061098152665, err=11.969979682593467 u[5,2]=16.064555742223146, U=2.7182818284590455, err=13.3462739137641 u[5,3]=16.846474796059674, U=2.878135984906894, err=13.96833881115278 u[5,4]=0.0, U=3.0473906939634254, err=-3.0473906939634254 u[5,5]=0.0, U=3.2265987744687123, err=-3.2265987744687123 u[5,6]=0.0, U=3.4163455549122808, err=-3.4163455549122808 u[6,1]=0.0, U=2.7182818284590455, err=-2.7182818284590455 u[6,2]=0.0, U=2.878135984906894, err=-2.878135984906894 u[6,3]=0.0, U=3.0473906939634254, err=-3.0473906939634254 u[6,4]=0.0, U=3.2265987744687132, err=-3.2265987744687132 u[6,5]=0.0, U=3.4163455549122808, err=-3.4163455549122808 u[6,6]=0.0, U=3.617250785229937, err=-3.617250785229937 nx=8, ny=8, np=5 maxerr=2230.0474971809945, avgerr=447.9195133500407 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=8, ny=8 calling gauleg xmin=1.0, xmax=3.0, npx=6 calling gauleg ymin=1.0, ymax=2.0, npy=6 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=2.042727070264908, U=2.042727070266142, err=-1.234123914173324E-12 u[1,2]=2.162853839043701, U=2.162853839040405, err=3.2960301155071647E-12 u[1,3]=2.2900449096387883, U=2.290044909642452, err=-3.6637359812630166E-12 u[1,4]=2.424715712874192, U=2.4247157128777834, err=-3.5913494400574564E-12 u[1,5]=2.567306109818801, U=2.5673061098152665, err=3.5345060211966484E-12 u[1,6]=2.7182818284576795, U=2.7182818284590455, err=-1.3660184094987926E-12 u[2,1]=2.1628538390431844, U=2.162853839040405, err=2.779554364451542E-12 u[2,2]=2.2900449096489077, U=2.290044909642452, err=6.45572484359036E-12 u[2,3]=2.4247157128793226, U=2.4247157128777834, err=1.539213201340317E-12 u[2,4]=2.5673061098172343, U=2.5673061098152665, err=1.9677592888456275E-12 u[2,5]=2.718281828466472, U=2.7182818284590455, err=7.426503856322597E-12 u[2,6]=2.8781359849107853, U=2.878135984906894, err=3.891109656706249E-12 u[3,1]=2.2900449096397693, U=2.290044909642452, err=-2.6827429167042283E-12 u[3,2]=2.4247157128797125, U=2.4247157128777834, err=1.929123527588672E-12 u[3,3]=2.5673061098088255, U=2.5673061098152665, err=-6.441069899665308E-12 u[3,4]=2.7182818284525205, U=2.7182818284590455, err=-6.52500276032697E-12 u[3,5]=2.87813598490861, U=2.878135984906894, err=1.715960706860642E-12 u[3,6]=3.0473906939600637, U=3.0473906939634254, err=-3.361755318564974E-12 u[4,1]=2.4247157128750727, U=2.4247157128777834, err=-2.7107205369247822E-12 u[4,2]=2.5673061098175185, U=2.5673061098152665, err=2.2519763831496675E-12 u[4,3]=2.718281828452475, U=2.7182818284590455, err=-6.5707439489415265E-12 u[4,4]=2.8781359849002173, U=2.878135984906894, err=-6.6768812700956914E-12 u[4,5]=3.047390693965427, U=3.0473906939634254, err=2.0015100687942322E-12 u[4,6]=3.2265987744653035, U=3.2265987744687132, err=-3.4097169532287808E-12 u[5,1]=2.567306109818181, U=2.5673061098152665, err=2.914557484245961E-12 u[5,2]=2.7182818284662487, U=2.7182818284590455, err=7.203126983768016E-12 u[5,3]=2.878135984908249, U=2.878135984906894, err=1.354916179252541E-12 u[5,4]=3.047390693965155, U=3.0473906939634254, err=1.7297274723659939E-12 u[5,5]=3.2265987744768543, U=3.2265987744687123, err=8.141931573391048E-12 u[5,6]=3.416345554916168, U=3.4163455549122808, err=3.887112853817598E-12 u[6,1]=2.7182818284576, U=2.7182818284590455, err=-1.4455103780619538E-12 u[6,2]=2.878135984911574, U=2.878135984906894, err=4.67981209339996E-12 u[6,3]=3.0473906939588606, U=3.0473906939634254, err=-4.564792988048794E-12 u[6,4]=3.2265987744642315, U=3.2265987744687132, err=-4.481748305806832E-12 u[6,5]=3.416345554917152, U=3.4163455549122808, err=4.871214542845337E-12 u[6,6]=3.6172507852282507, U=3.617250785229937, err=-1.6862067298006878E-12 nx=8, ny=8, np=6 maxerr=8.141931573391048E-12, avgerr=2.0950567669597575E-12 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=8, ny=8 calling gauleg xmin=1.0, xmax=3.0, npx=7 calling gauleg ymin=1.0, ymax=2.0, npy=7 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=2.0427270702637657, U=2.042727070266142, err=-2.376321361907685E-12 u[1,2]=2.162853839040967, U=2.162853839040405, err=5.622169396701793E-13 u[1,3]=2.2900449096401787, U=2.290044909642452, err=-2.2732926652224705E-12 u[1,4]=2.4247157128753707, U=2.4247157128777834, err=-2.41273667711539E-12 u[1,5]=2.567306109815689, U=2.5673061098152665, err=4.2232883856740955E-13 u[1,6]=2.7182818284564543, U=2.7182818284590455, err=-2.5912605394751154E-12 u[2,1]=2.1628538390403658, U=2.162853839040405, err=-3.907985046680551E-14 u[2,2]=2.290044909645825, U=2.290044909642452, err=3.3728575488112256E-12 u[2,3]=2.424715712878885, U=2.4247157128777834, err=1.1017853296380054E-12 u[2,4]=2.567306109816421, U=2.5673061098152665, err=1.1546319456101628E-12 u[2,5]=2.7182818284627386, U=2.7182818284590455, err=3.693045869113121E-12 u[2,6]=2.8781359849072925, U=2.878135984906894, err=3.9834802123550617E-13 u[3,1]=2.290044909640281, U=2.290044909642452, err=-2.171152146956956E-12 u[3,2]=2.4247157128787915, U=2.4247157128777834, err=1.0080825063596421E-12 u[3,3]=2.567306109813406, U=2.5673061098152665, err=-1.8607337892717624E-12 u[3,4]=2.7182818284570605, U=2.7182818284590455, err=-1.98507876802978E-12 u[3,5]=2.8781359849078427, U=2.878135984906894, err=9.485745522397337E-13 u[3,6]=3.047390693961186, U=3.0473906939634254, err=-2.2395418852738658E-12 u[4,1]=2.4247157128753623, U=2.4247157128777834, err=-2.4211743721025414E-12 u[4,2]=2.56730610981634, U=2.5673061098152665, err=1.0733636202076013E-12 u[4,3]=2.7182818284569827, U=2.7182818284590455, err=-2.062794379753541E-12 u[4,4]=2.8781359849046892, U=2.878135984906894, err=-2.204902926905561E-12 u[4,5]=3.047390693964392, U=3.0473906939634254, err=9.667822098435863E-13 u[4,6]=3.226598774466174, U=3.2265987744687132, err=-2.539302101922658E-12 u[5,1]=2.5673061098149432, U=2.5673061098152665, err=-3.232969447708456E-13 u[5,2]=2.718281828462691, U=2.7182818284590455, err=3.645528323659164E-12 u[5,3]=2.8781359849078334, U=2.878135984906894, err=9.392486788328824E-13 u[5,4]=3.0473906939643545, U=3.0473906939634254, err=9.29034627006331E-13 u[5,5]=3.2265987744726012, U=3.2265987744687123, err=3.888889210656998E-12 u[5,6]=3.4163455549123074, U=3.4163455549122808, err=2.6645352591003757E-14 u[6,1]=2.7182818284563077, U=2.7182818284590455, err=-2.737809978725636E-12 u[6,2]=2.8781359849080665, U=2.878135984906894, err=1.1723955140041653E-12 u[6,3]=3.0473906939609665, U=3.0473906939634254, err=-2.4589219549397967E-12 u[6,4]=3.226598774466033, U=3.2265987744687132, err=-2.680078381445128E-12 u[6,5]=3.416345554913187, U=3.4163455549122808, err=9.063860773039778E-13 u[6,6]=3.617250785226929, U=3.617250785229937, err=-3.007816218314474E-12 nx=8, ny=8, np=7 maxerr=3.888889210656998E-12, avgerr=1.0101607050838624E-12 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=8, ny=8 calling gauleg xmin=1.0, xmax=3.0, npx=8 calling gauleg ymin=1.0, ymax=2.0, npy=8 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=2.0427270702638767, U=2.042727070266142, err=-2.2652990594451694E-12 u[1,2]=2.1628538390411287, U=2.162853839040405, err=7.238654120556021E-13 u[1,3]=2.290044909640363, U=2.290044909642452, err=-2.0889956431346945E-12 u[1,4]=2.4247157128755323, U=2.4247157128777834, err=-2.2510882047299674E-12 u[1,5]=2.567306109815725, U=2.5673061098152665, err=4.583000645652646E-13 u[1,6]=2.718281828456513, U=2.7182818284590455, err=-2.532640763774907E-12 u[2,1]=2.162853839040532, U=2.162853839040405, err=1.270095140171179E-13 u[2,2]=2.2900449096461593, U=2.290044909642452, err=3.707256723828323E-12 u[2,3]=2.4247157128792596, U=2.4247157128777834, err=1.4761525335416081E-12 u[2,4]=2.5673061098166725, U=2.5673061098152665, err=1.4059864383852982E-12 u[2,5]=2.7182818284628145, U=2.7182818284590455, err=3.7689851239974814E-12 u[2,6]=2.8781359849072454, U=2.878135984906894, err=3.5127456499139953E-13 u[3,1]=2.290044909640427, U=2.290044909642452, err=-2.0250467969162855E-12 u[3,2]=2.4247157128790344, U=2.4247157128777834, err=1.2509993041476264E-12 u[3,3]=2.5673061098136545, U=2.5673061098152665, err=-1.6120438317557273E-12 u[3,4]=2.718281828457283, U=2.7182818284590455, err=-1.7625900738948985E-12 u[3,5]=2.8781359849079178, U=2.878135984906894, err=1.0236256287043943E-12 u[3,6]=3.0473906939611006, U=3.0473906939634254, err=-2.3248070135650778E-12 u[4,1]=2.4247157128754786, U=2.4247157128777834, err=-2.304822999121825E-12 u[4,2]=2.5673061098163634, U=2.5673061098152665, err=1.0969003483296547E-12 u[4,3]=2.718281828457012, U=2.7182818284590455, err=-2.0334844919034367E-12 u[4,4]=2.878135984904834, U=2.878135984906894, err=-2.0601298444944405E-12 u[4,5]=3.047390693964518, U=3.0473906939634254, err=1.092459456231154E-12 u[4,6]=3.226598774466267, U=3.2265987744687132, err=-2.446043367854145E-12 u[5,1]=2.567306109814976, U=2.5673061098152665, err=-2.9043434324194095E-13 u[5,2]=2.7182818284626684, U=2.7182818284590455, err=3.622879773956811E-12 u[5,3]=2.878135984907763, U=2.878135984906894, err=8.686384944667225E-13 u[5,4]=3.047390693964393, U=3.0473906939634254, err=9.676703882632864E-13 u[5,5]=3.226598774472739, U=3.2265987744687123, err=4.026556865710518E-12 u[5,6]=3.416345554912418, U=3.4163455549122808, err=1.3722356584366935E-13 u[6,1]=2.7182818284562575, U=2.7182818284590455, err=-2.787992059438693E-12 u[6,2]=2.8781359849080483, U=2.878135984906894, err=1.1541878564003127E-12 u[6,3]=3.047390693960927, U=3.0473906939634254, err=-2.4984458946164523E-12 u[6,4]=3.2265987744660634, U=3.2265987744687132, err=-2.6498803151753236E-12 u[6,5]=3.416345554913232, U=3.4163455549122808, err=9.512390874988341E-13 u[6,6]=3.617250785226909, U=3.617250785229937, err=-3.027800232757727E-12 nx=8, ny=8, np=8 maxerr=4.026556865710518E-12, avgerr=1.0197016842017348E-12 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=10, ny=10 calling gauleg xmin=1.0, xmax=3.0, npx=8 calling gauleg ymin=1.0, ymax=2.0, npy=8 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=1.9915015239940324, U=1.9915015239946179, err=-5.855316231873076E-13 u[1,2]=2.0820090840771073, U=2.0820090840784555, err=-1.3482548411047901E-12 u[1,3]=2.1766299317137787, U=2.1766299317162483, err=-2.4695800959761982E-12 u[1,4]=2.2755510030522426, U=2.275551003054389, err=-2.1462831512053526E-12 u[1,5]=2.3789677299064222, U=2.378967729906635, err=-2.1271873151818E-13 u[1,6]=2.4870844258565667, U=2.487084425855805, err=7.616129948928574E-13 u[1,7]=2.600114689902772, U=2.6001146899026075, err=1.6431300764452317E-13 u[1,8]=2.718281828458907, U=2.7182818284590455, err=-1.3855583347321954E-13 u[2,1]=2.082009084077073, U=2.0820090840784555, err=-1.382449710263245E-12 u[2,2]=2.1766299317133266, U=2.1766299317162483, err=-2.921662911603562E-12 u[2,3]=2.2755510030509183, U=2.275551003054389, err=-3.4705571749782393E-12 u[2,4]=2.3789677299049856, U=2.3789677299066345, err=-1.6489032361732825E-12 u[2,5]=2.4870844258566573, U=2.487084425855805, err=8.522071937022702E-13 u[2,6]=2.6001146899037333, U=2.6001146899026075, err=1.1257661469699087E-12 u[2,7]=2.7182818284589696, U=2.7182818284590455, err=-7.593925488436071E-14 u[2,8]=2.841819296519697, U=2.841819296520117, err=-4.2010839251815923E-13 u[3,1]=2.176629931714049, U=2.1766299317162483, err=-2.19912976717751E-12 u[3,2]=2.275551003050244, U=2.275551003054389, err=-4.144684595530634E-12 u[3,3]=2.3789677299018717, U=2.3789677299066345, err=-4.7628567756419216E-12 u[3,4]=2.4870844258528795, U=2.487084425855805, err=-2.9256597144922125E-12 u[3,5]=2.6001146899021332, U=2.6001146899026075, err=-4.742872761198669E-13 u[3,6]=2.718281828458864, U=2.7182818284590455, err=-1.816324868286756E-13 u[3,7]=2.841819296518887, U=2.8418192965201166, err=-1.2296830220748234E-12 u[3,8]=2.970971158884611, U=2.9709711588854004, err=-7.895906151134113E-13 u[4,1]=2.275551003052744, U=2.275551003054389, err=-1.644906433284632E-12 u[4,2]=2.378967729903324, U=2.378967729906635, err=-3.311129148642067E-12 u[4,3]=2.487084425852151, U=2.487084425855805, err=-3.653966018646315E-12 u[4,4]=2.6001146898998826, U=2.6001146899026075, err=-2.7249313916399842E-12 u[4,5]=2.7182818284574024, U=2.7182818284590455, err=-1.6431300764452317E-12 u[4,6]=2.8418192965190303, U=2.8418192965201166, err=-1.0862422072932532E-12 u[4,7]=2.970971158884524, U=2.9709711588854004, err=-8.766321002440236E-13 u[4,8]=3.1059925723411506, U=3.10599257234172, err=-5.693223670277803E-13 u[5,1]=2.3789677299053014, U=2.378967729906635, err=-1.333599897179738E-12 u[5,2]=2.4870844258541402, U=2.487084425855805, err=-1.6648904477278847E-12 u[5,3]=2.6001146899015155, U=2.6001146899026075, err=-1.092015367021304E-12 u[5,4]=2.718281828457894, U=2.7182818284590455, err=-1.1515233211412124E-12 u[5,5]=2.8418192965184934, U=2.841819296520117, err=-1.623590151211829E-12 u[5,6]=2.970971158884392, U=2.9709711588854004, err=-1.0085265955694922E-12 u[5,7]=3.105992572341687, U=3.10599257234172, err=-3.2862601528904634E-14 u[5,8]=3.2471502897593036, U=3.247150289759531, err=-2.2737367544323206E-13 u[6,1]=2.487084425855204, U=2.487084425855805, err=-6.012967901369848E-13 u[6,2]=2.600114689901704, U=2.6001146899026075, err=-9.037215420448774E-13 u[6,3]=2.718281828458142, U=2.7182818284590455, err=-9.037215420448774E-13 u[6,4]=2.841819296518691, U=2.8418192965201166, err=-1.425526363618701E-12 u[6,5]=2.9709711588835446, U=2.9709711588854004, err=-1.8558488079634117E-12 u[6,6]=3.105992572340269, U=3.10599257234172, err=-1.4508394485801546E-12 u[6,7]=3.2471502897586504, U=3.24715028975953, err=-8.79740724712974E-13 u[6,8]=3.3947231870982106, U=3.394723187098903, err=-6.923350781562476E-13 u[7,1]=2.600114689902088, U=2.6001146899026075, err=-5.195843755245733E-13 u[7,2]=2.718281828457761, U=2.7182818284590455, err=-1.2847500840962311E-12 u[7,3]=2.8418192965178886, U=2.8418192965201166, err=-2.227995565817764E-12 u[7,4]=2.970971158882734, U=2.9709711588854004, err=-2.666311615939776E-12 u[7,5]=3.105992572339099, U=3.10599257234172, err=-2.6210145165350696E-12 u[7,6]=3.247150289757075, U=3.24715028975953, err=-2.454925152051146E-12 u[7,7]=3.3947231870968295, U=3.394723187098903, err=-2.0734525207899424E-12 u[7,8]=3.5490028143651884, U=3.549002814366304, err=-1.1155520951433573E-12 u[8,1]=2.7182818284582404, U=2.7182818284590455, err=-8.051337374581635E-13 u[8,2]=2.8418192965189357, U=2.841819296520117, err=-1.1812772982011666E-12 u[8,3]=2.970971158884016, U=2.9709711588854004, err=-1.3842260671026452E-12 u[8,4]=3.1059925723399817, U=3.10599257234172, err=-1.738165167353145E-12 u[8,5]=3.2471502897575024, U=3.247150289759531, err=-2.028599510595086E-12 u[8,6]=3.3947231870971057, U=3.394723187098903, err=-1.7972290322632034E-12 u[8,7]=3.5490028143651773, U=3.549002814366304, err=-1.1266543253896089E-12 u[8,8]=3.7102939716101275, U=3.7102939716106484, err=-5.209166431541234E-13 nx=10, ny=10, np=8 maxerr=4.7628567756419216E-12, avgerr=9.677614265513057E-13 laphi instantiated fem_check22e_la.java running Given: uxx(x,y)+uyy(x,y)+r(x,y)*u(x,y)=f(x,y) r(x,y)=sin(x)+cos(y) f(x,y)=exp((x+2*y)/5)/5 +(sin(x)+cos(y))*exp((x+2*y)/5) xmin<=x<=xmax ymin<=y<=ymax Boundaries Analytic solution u(x,y)=exp((x+2*y)/5) xmin=1.0, xmax=3.0, ymin=1.0, ymax=2.0 nx=10, ny=10 calling gauleg xmin=1.0, xmax=3.0, npx=9 calling gauleg ymin=1.0, ymax=2.0, npy=9 compute stiffness matrix k computed stiffness matrix f computed forcing vector solving k u = f for u u computed Galerkin, U analytic, error u[1,1]=1.9915015239959561, U=1.9915015239946179, err=1.3382628338831637E-12 u[1,2]=2.082009084082623, U=2.0820090840784555, err=4.1673331452329876E-12 u[1,3]=2.176629931722804, U=2.1766299317162483, err=6.555644915806624E-12 u[1,4]=2.275551003062175, U=2.275551003054389, err=7.786216116301148E-12 u[1,5]=2.378967729913827, U=2.378967729906635, err=7.192024753521764E-12 u[1,6]=2.487084425861498, U=2.487084425855805, err=5.692779581067953E-12 u[1,7]=2.6001146899065, U=2.6001146899026075, err=3.892441924335799E-12 u[1,8]=2.718281828461379, U=2.7182818284590455, err=2.333244708552229E-12 u[2,1]=2.082009084082016, U=2.0820090840784555, err=3.560263195367952E-12 u[2,2]=2.1766299317243845, U=2.1766299317162483, err=8.136158413662997E-12 u[2,3]=2.275551003067713, U=2.275551003054389, err=1.3324008563131429E-11 u[2,4]=2.3789677299224343, U=2.3789677299066345, err=1.5799805908045528E-11 u[2,5]=2.487084425870527, U=2.487084425855805, err=1.4722001395739426E-11 u[2,6]=2.6001146899144048, U=2.6001146899026075, err=1.1797229859666913E-11 u[2,7]=2.718281828467684, U=2.7182818284590455, err=8.638423310003418E-12 u[2,8]=2.8418192965248603, U=2.841819296520117, err=4.743316850408519E-12 u[3,1]=2.176629931720259, U=2.1766299317162483, err=4.0105696541559155E-12 u[3,2]=2.275551003063197, U=2.275551003054389, err=8.808065388166142E-12 u[3,3]=2.3789677299211647, U=2.3789677299066345, err=1.4530154857084199E-11 u[3,4]=2.4870844258748916, U=2.487084425855805, err=1.908651015014584E-11 u[3,5]=2.600114689922234, U=2.6001146899026075, err=1.9626522629323517E-11 u[3,6]=2.7182818284746344, U=2.7182818284590455, err=1.5588863533366748E-11 u[3,7]=2.8418192965299256, U=2.8418192965201166, err=9.809042467168183E-12 u[3,8]=2.970971158890338, U=2.9709711588854004, err=4.937383835112996E-12 u[4,1]=2.275551003056669, U=2.275551003054389, err=2.2799540033702215E-12 u[4,2]=2.3789677299117247, U=2.378967729906635, err=5.089706434091568E-12 u[4,3]=2.48708442586475, U=2.487084425855805, err=8.944844864799961E-12 u[4,4]=2.600114689915998, U=2.6001146899026075, err=1.3390621944608938E-11 u[4,5]=2.7182818284745225, U=2.7182818284590455, err=1.5476953052484532E-11 u[4,6]=2.841819296532947, U=2.8418192965201166, err=1.2830625450988009E-11 u[4,7]=2.970971158893327, U=2.9709711588854004, err=7.926548306613768E-12 u[4,8]=3.1059925723457043, U=3.10599257234172, err=3.984368390774762E-12 u[5,1]=2.3789677299069805, U=2.378967729906635, err=3.455014052633487E-13 u[5,2]=2.48708442585662, U=2.487084425855805, err=8.149037000748649E-13 u[5,3]=2.600114689904882, U=2.6001146899026075, err=2.2746249328520207E-12 u[5,4]=2.7182818284639296, U=2.7182818284590455, err=4.884093129930989E-12 u[5,5]=2.8418192965272806, U=2.841819296520117, err=7.16360304409136E-12 u[5,6]=2.9709711588932115, U=2.9709711588854004, err=7.811085112052751E-12 u[5,7]=3.105992572348035, U=3.10599257234172, err=6.31494856406789E-12 u[5,8]=3.247150289762949, U=3.247150289759531, err=3.418154648215932E-12 u[6,1]=2.4870844258555924, U=2.487084425855805, err=-2.1271873151818E-13 u[6,2]=2.600114689902936, U=2.6001146899026075, err=3.2862601528904634E-13 u[6,3]=2.7182818284599612, U=2.7182818284590455, err=9.157119507108291E-13 u[6,4]=2.8418192965221465, U=2.8418192965201166, err=2.0299317782246362E-12 u[6,5]=2.970971158889454, U=2.9709711588854004, err=4.0536463075113716E-12 u[6,6]=3.1059925723473056, U=3.10599257234172, err=5.5857540814940876E-12 u[6,7]=3.2471502897645457, U=3.24715028975953, err=5.015543536046607E-12 u[6,8]=3.3947231871015173, U=3.394723187098903, err=2.6143531783873186E-12 u[7,1]=2.600114689903404, U=2.6001146899026075, err=7.966960424710123E-13 u[7,2]=2.718281828461139, U=2.7182818284590455, err=2.093436535233195E-12 u[7,3]=2.8418192965228064, U=2.8418192965201166, err=2.6898483440618293E-12 u[7,4]=2.970971158888391, U=2.9709711588854004, err=2.9904967391303217E-12 u[7,5]=3.105992572345528, U=3.10599257234172, err=3.808064974464287E-12 u[7,6]=3.247150289763683, U=3.24715028975953, err=4.1526782013079355E-12 u[7,7]=3.3947231871019707, U=3.394723187098903, err=3.0677682616442326E-12 u[7,8]=3.5490028143676655, U=3.549002814366304, err=1.361577517400292E-12 u[8,1]=2.7182818284600083, U=2.7182818284590455, err=9.627854069549358E-13 u[8,2]=2.8418192965217197, U=2.841819296520117, err=1.602717958348876E-12 u[8,3]=2.970971158887162, U=2.9709711588854004, err=1.7617018954751984E-12 u[8,4]=3.1059925723430397, U=3.10599257234172, err=1.319833131674386E-12 u[8,5]=3.247150289760308, U=3.247150289759531, err=7.771561172376096E-13 u[8,6]=3.3947231870999977, U=3.394723187098903, err=1.0946799022804043E-12 u[8,7]=3.549002814367771, U=3.549002814366304, err=1.4672707493446069E-12 u[8,8]=3.7102939716113967, U=3.7102939716106484, err=7.482903185973555E-13 nx=10, ny=10, np=9 maxerr=1.9626522629323517E-11, avgerr=3.717330887553771E-12