fem_check33_la.f90 running solve uxxx(x,y,z) + 2 uyyy(x,y,z) + 3 uzzz(x,y,z) + 4 uxxy(x,y,z) + 5 uxxz(x,y,z) + 6 uyyx(x,y,z) + 7 uyyz(x,y,z) + 8 uzzx(x,y,z) + 9 uzzy(x,y,z) + 10 uxx(x,y,z) + 11 uyy(x,y,z) + 12 uzz(x,y,z) + 13 uxy(x,y,z) + 14 uxz(x,y,z) + 15 uyz(x,y,z) + 16 ux(x,y,z) + 17 uy(x,y,z) + 18 uz(x,y,z) + 19 u(x,y,z) = F(x,y,z) F(x,y,z) = 406.0 + 208.0*x*y*z*z + 240.0*x*x*y*z + 88.0*x*x*z*z + 136.0*x*x*y*z*z + 128.0*x*y*y*z*z + 217.0*x + 302.0*y + 80.0*y*y*z*z + 144.0*x*x*y*y*z + 96.0*x*x*y*y + 224.0*x*y*y*z + 76.0*x*x*y*y*z*z + 144.0*x*x*y + 80.0*y*y*z + 64.0*y*z*z + 133.0*y*z + 128.0*x*y*y + 112.0*x*x*z + 96.0*x*z*z + 114.0*x*z + 95.0*x*y + 431.0*z + 19.0*x*x*x*x + 38.0*y*y*y*y + 57.0*z*z*z*z + 64.0*x*x*x + 136.0*y*y*y + 216.0*z*z*z + 120.0*x*x + 264.0*y*y + 432.0*z*z boundary conditions computed using u(x,y,z) analytic solution may be given by u(x,y,z) = x**4 + 2 y**4 + 3 z**4 + 4 x**2 y**2 z**2 + 5 x y + 6 x z + 7 y z + 8 Gauss-Legendre integration used xmin= 0.00000000000000 , ymin = 0.00000000000000 , zmin= 0.00000000000000 xmax= 1.00000000000000 , ymax = 1.00000000000000 , zmax= 1.00000000000000 nx= 5 , ny = 5 , nz = 5 x grid and analytic solution, at ymin,zmin i= 1 , Ua( 0.00000000000000 )= 8.00000000000000 i= 2 , Ua( 0.250000000000000 )= 8.00390625000000 i= 3 , Ua( 0.500000000000000 )= 8.06250000000000 i= 4 , Ua( 0.750000000000000 )= 8.31640625000000 i= 5 , Ua( 1.00000000000000 )= 9.00000000000000 y grid and analytic solution, at xmin,zmin ii= 1 , Ua( 0.00000000000000 )= 8.00000000000000 ii= 2 , Ua( 0.250000000000000 )= 8.00781250000000 ii= 3 , Ua( 0.500000000000000 )= 8.12500000000000 ii= 4 , Ua( 0.750000000000000 )= 8.63281250000000 ii= 5 , Ua( 1.00000000000000 )= 10.0000000000000 z grid and analytic solution, at xmin,ymin iii= 1 , Ua( 0.00000000000000 )= 8.00000000000000 iii= 2 , Ua( 0.250000000000000 )= 8.01171875000000 iii= 3 , Ua( 0.500000000000000 )= 8.18750000000000 iii= 4 , Ua( 0.750000000000000 )= 8.94921875000000 iii= 5 , Ua( 1.00000000000000 )= 11.0000000000000 calling gaulegf npx= 12 calling gaulegf npy= 12 calling gaulegf npz= 12 xx(1)= 9.219682876640378E-003 , xx(2)= 4.794137181476255E-002 , wx(1)= 2.358766819325422E-002 , wx(2)= 5.346966299765921E-002 yy(1)= 9.219682876640378E-003 , yy(2)= 4.794137181476255E-002 , wy(1)= 2.358766819325422E-002 , wy(2)= 5.346966299765921E-002 zz(1)= 9.219682876640378E-003 , zz(2)= 4.794137181476255E-002 , wz(1)= 2.358766819325422E-002 , wz(2)= 5.346966299765921E-002 galk(xx(3),yy(3),zz(3),2,2,2,2,2,2)= -12973.4152642125 galf(xx(3),yy(3),zz(3),2,2,2)= 637.302707749288 compute stiffness matrix Legendre integration= 3.92786 at i=2, j=1, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 30.83426 at i=2, j=2, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 4.70871 at i=2, j=3, ii=5, jj=6, iii=5,jjj=6 Legendre integration= -0.40201 at i=2, j=4, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 3.05964 at i=2, j=5, ii=5, jj=6, iii=5,jjj=6 Legendre integration= -2.17733 at i=3, j=1, ii=5, jj=6, iii=5,jjj=6 Legendre integration= -9.28356 at i=3, j=2, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 29.83269 at i=3, j=3, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 5.05755 at i=3, j=4, ii=5, jj=6, iii=5,jjj=6 Legendre integration= -7.63118 at i=3, j=5, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 0.50573 at i=4, j=1, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 6.20171 at i=4, j=2, ii=5, jj=6, iii=5,jjj=6 Legendre integration= -8.93472 at i=4, j=3, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 30.21410 at i=4, j=4, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 14.14164 at i=4, j=5, ii=5, jj=6, iii=5,jjj=6 Legendre integration= 91.44553 F at i=2, ii=5, iii=5 Legendre integration= 36.71149 F at i=3, ii=5, iii=5 Legendre integration= 125.97343 F at i=4, ii=5, iii=5 k computed stiffness matrix, see above f computed forcing function, see above ug computed Galerkin, Ua analytic, error ug(1,1,1)= 8.0000, Ua= 8.0000, err= 0.1509903E-12 ug(1,1,2)= 8.0117, Ua= 8.0117, err= 0.2131628E-13 ug(1,1,3)= 8.1875, Ua= 8.1875, err= -0.1190159E-12 ug(1,1,4)= 8.9492, Ua= 8.9492, err= 0.4618528E-13 ug(1,1,5)=11.0000, Ua=11.0000, err= 0.0000000E+00 ug(1,2,1)= 8.0078, Ua= 8.0078, err= 0.4263256E-13 ug(1,2,2)= 8.4570, Ua= 8.4570, err= -0.1776357E-13 ug(1,2,3)= 9.0703, Ua= 9.0703, err= 0.0000000E+00 ug(1,2,4)=10.2695, Ua=10.2695, err= -0.5329071E-13 ug(1,2,5)=12.7578, Ua=12.7578, err= 0.1776357E-14 ug(1,3,1)= 8.1250, Ua= 8.1250, err= -0.6927792E-13 ug(1,3,2)= 9.0117, Ua= 9.0117, err= -0.5861978E-13 ug(1,3,3)=10.0625, Ua=10.0625, err= 0.8881784E-14 ug(1,3,4)=11.6992, Ua=11.6992, err= -0.1101341E-12 ug(1,3,5)=14.6250, Ua=14.6250, err= 0.0000000E+00 ug(1,4,1)= 8.6328, Ua= 8.6328, err= -0.4440892E-13 ug(1,4,2)= 9.9570, Ua= 9.9570, err= -0.9237056E-13 ug(1,4,3)=11.4453, Ua=11.4453, err= -0.8348877E-13 ug(1,4,4)=13.5195, Ua=13.5195, err= 0.6217249E-13 ug(1,4,5)=16.8828, Ua=16.8828, err= 0.0000000E+00 ug(1,5,1)=10.0000, Ua=10.0000, err= 0.0000000E+00 ug(1,5,2)=11.7617, Ua=11.7617, err= 0.0000000E+00 ug(1,5,3)=13.6875, Ua=13.6875, err= 0.0000000E+00 ug(1,5,4)=16.1992, Ua=16.1992, err= 0.0000000E+00 ug(1,5,5)=20.0000, Ua=20.0000, err= 0.0000000E+00 ug(2,1,1)= 8.0039, Ua= 8.0039, err= -0.5329071E-13 ug(2,1,2)= 8.3906, Ua= 8.3906, err= -0.4440892E-13 ug(2,1,3)= 8.9414, Ua= 8.9414, err= 0.4263256E-13 ug(2,1,4)=10.0781, Ua=10.0781, err= 0.3907985E-12 ug(2,1,5)=12.5039, Ua=12.5039, err= 0.0000000E+00 ug(2,2,1)= 8.3242, Ua= 8.3242, err= 0.2327027E-12 ug(2,2,2)= 9.1494, Ua= 9.1494, err= 0.3677059E-12 ug(2,2,3)=10.1406, Ua=10.1406, err= -0.2664535E-13 ug(2,2,4)=11.7197, Ua=11.7197, err= 0.2291500E-12 ug(2,2,5)=14.5898, Ua=14.5898, err= 0.1740830E-12 ug(2,3,1)= 8.7539, Ua= 8.7539, err= -0.2469136E-12 ug(2,3,2)=10.0195, Ua=10.0195, err= -0.3161915E-12 ug(2,3,3)=11.4570, Ua=11.4570, err= 0.1776357E-13 ug(2,3,4)=13.4883, Ua=13.4883, err= -0.1119105E-12 ug(2,3,5)=16.8164, Ua=16.8164, err= 0.3907985E-13 ug(2,4,1)= 9.5742, Ua= 9.5742, err= 0.2664535E-13 ug(2,4,2)=11.2822, Ua=11.2822, err= -0.1243450E-12 ug(2,4,3)=13.1719, Ua=13.1719, err= 0.6394885E-13 ug(2,4,4)=15.6650, Ua=15.6650, err= -0.3907985E-13 ug(2,4,5)=19.4648, Ua=19.4648, err= 0.7105427E-14 ug(2,5,1)=11.2539, Ua=11.2539, err= 0.0000000E+00 ug(2,5,2)=13.4062, Ua=13.4063, err= -0.2309264E-13 ug(2,5,3)=15.7539, Ua=15.7539, err= 0.2273737E-12 ug(2,5,4)=18.7187, Ua=18.7188, err= -0.7105427E-14 ug(2,5,5)=23.0039, Ua=23.0039, err= 0.0000000E+00 ug(3,1,1)= 8.0625, Ua= 8.0625, err= 0.9592327E-13 ug(3,1,2)= 8.8242, Ua= 8.8242, err= -0.7105427E-14 ug(3,1,3)= 9.7500, Ua= 9.7500, err= -0.2309264E-13 ug(3,1,4)=11.2617, Ua=11.2617, err= -0.1243450E-13 ug(3,1,5)=14.0625, Ua=14.0625, err= 0.2842171E-13 ug(3,2,1)= 8.6953, Ua= 8.6953, err= 0.9414691E-13 ug(3,2,2)= 9.8984, Ua= 9.8984, err= 0.8562040E-12 ug(3,2,3)=11.2734, Ua=11.2734, err= 0.4352074E-12 ug(3,2,4)=13.2422, Ua=13.2422, err= 0.2700062E-12 ug(3,2,5)=16.5078, Ua=16.5078, err= -0.3197442E-13 ug(3,3,1)= 9.4375, Ua= 9.4375, err= 0.1953993E-13 ug(3,3,2)=11.0898, Ua=11.0898, err= 0.5790923E-12 ug(3,3,3)=12.9375, Ua=12.9375, err= 0.4405365E-12 ug(3,3,4)=15.4023, Ua=15.4023, err= 0.2042810E-12 ug(3,3,5)=19.1875, Ua=19.1875, err= -0.1776357E-13 ug(3,4,1)=10.5703, Ua=10.5703, err= -0.1545430E-12 ug(3,4,2)=12.6797, Ua=12.6797, err= -0.1367795E-12 ug(3,4,3)=15.0234, Ua=15.0234, err= 0.2913225E-12 ug(3,4,4)=18.0234, Ua=18.0234, err= 0.6394885E-13 ug(3,4,5)=22.3828, Ua=22.3828, err= 0.1065814E-13 ug(3,5,1)=12.5625, Ua=12.5625, err= 0.0000000E+00 ug(3,5,2)=15.1367, Ua=15.1367, err= 0.1776357E-13 ug(3,5,3)=18.0000, Ua=18.0000, err= 0.7105427E-14 ug(3,5,4)=21.5742, Ua=21.5742, err= 0.0000000E+00 ug(3,5,5)=26.5625, Ua=26.5625, err= 0.3197442E-13 ug(4,1,1)= 8.3164, Ua= 8.3164, err= 0.0000000E+00 ug(4,1,2)= 9.4531, Ua= 9.4531, err= -0.1065814E-13 ug(4,1,3)=10.7539, Ua=10.7539, err= 0.5329071E-14 ug(4,1,4)=12.6406, Ua=12.6406, err= 0.0000000E+00 ug(4,1,5)=15.8164, Ua=15.8164, err= 0.0000000E+00 ug(4,2,1)= 9.2617, Ua= 9.2617, err= 0.0000000E+00 ug(4,2,2)=10.8447, Ua=10.8447, err= 0.4387601E-12 ug(4,2,3)=12.6094, Ua=12.6094, err= 0.3232969E-12 ug(4,2,4)=14.9775, Ua=14.9775, err= 0.7105427E-13 ug(4,2,5)=18.6523, Ua=18.6523, err= 0.0000000E+00 ug(4,3,1)=10.3164, Ua=10.3164, err= 0.3552714E-14 ug(4,3,2)=12.3633, Ua=12.3633, err= 0.8153478E-12 ug(4,3,3)=14.6445, Ua=14.6445, err= 0.6803447E-12 ug(4,3,4)=17.5820, Ua=17.5820, err= 0.3623768E-12 ug(4,3,5)=21.8789, Ua=21.8789, err= 0.0000000E+00 ug(4,4,1)=11.7617, Ua=11.7617, err= -0.5329071E-14 ug(4,4,2)=14.2900, Ua=14.2900, err= 0.3517187E-12 ug(4,4,3)=17.1406, Ua=17.1406, err= 0.4938272E-12 ug(4,4,4)=20.7354, Ua=20.7354, err= 0.4014566E-12 ug(4,4,5)=25.7773, Ua=25.7773, err= 0.0000000E+00 ug(4,5,1)=14.0664, Ua=14.0664, err= 0.0000000E+00 ug(4,5,2)=17.0938, Ua=17.0938, err= 0.0000000E+00 ug(4,5,3)=20.5664, Ua=20.5664, err= 0.0000000E+00 ug(4,5,4)=24.9063, Ua=24.9063, err= 0.0000000E+00 ug(4,5,5)=30.8164, Ua=30.8164, err= 0.0000000E+00 ug(5,1,1)= 9.0000, Ua= 9.0000, err= 0.0000000E+00 ug(5,1,2)=10.5117, Ua=10.5117, err= 0.0000000E+00 ug(5,1,3)=12.1875, Ua=12.1875, err= 0.0000000E+00 ug(5,1,4)=14.4492, Ua=14.4492, err= 0.0000000E+00 ug(5,1,5)=18.0000, Ua=18.0000, err= 0.0000000E+00 ug(5,2,1)=10.2578, Ua=10.2578, err= 0.0000000E+00 ug(5,2,2)=12.2227, Ua=12.2227, err= 0.0000000E+00 ug(5,2,3)=14.3828, Ua=14.3828, err= 0.0000000E+00 ug(5,2,4)=17.1602, Ua=17.1602, err= 0.0000000E+00 ug(5,2,5)=21.2578, Ua=21.2578, err= 0.0000000E+00 ug(5,3,1)=11.6250, Ua=11.6250, err= 0.0000000E+00 ug(5,3,2)=14.0742, Ua=14.0742, err= 0.0000000E+00 ug(5,3,3)=16.8125, Ua=16.8125, err= 0.0000000E+00 ug(5,3,4)=20.2617, Ua=20.2617, err= 0.0000000E+00 ug(5,3,5)=25.1250, Ua=25.1250, err= 0.0000000E+00 ug(5,4,1)=13.3828, Ua=13.3828, err= 0.0000000E+00 ug(5,4,2)=16.3477, Ua=16.3477, err= 0.0000000E+00 ug(5,4,3)=19.7578, Ua=19.7578, err= 0.0000000E+00 ug(5,4,4)=24.0352, Ua=24.0352, err= 0.0000000E+00 ug(5,4,5)=29.8828, Ua=29.8828, err= 0.0000000E+00 ug(5,5,1)=16.0000, Ua=16.0000, err= 0.0000000E+00 ug(5,5,2)=19.5117, Ua=19.5117, err= 0.0000000E+00 ug(5,5,3)=23.6875, Ua=23.6875, err= 0.0000000E+00 ug(5,5,4)=28.9492, Ua=28.9492, err= 0.0000000E+00 ug(5,5,5)=36.0000, Ua=36.0000, err= 0.0000000E+00 maxerr= 8.562039965909207E-013 , avgerr= 9.269740530726267E-014 end fem_check33_la.f90