fem_bihar2dps_la.f90 running solve uxxxx(x,y) + 2 uxxyy(x,y) + uyyyy(x,y) = F(x,y) F(x,y) = 4*sin(x)*sin(y) boundary conditions computed using ub(x,y) ub(x,y) = sin(x)*sin(y) high order shape functions used high order Gauss-Legendre quadrature used 49 Degrees of Freedom xmin= 0.00000000000000 , ymin = 0.00000000000000 xmax= 3.14159011840820 , ymax = 3.14159011840820 nx= 9 , ny = 9 x grid and analytic solution, at ymax i= 1 , ub( 0.00000000000000 , 3.14159011840820 )= 0.00000000000000 i= 2 , ub( 0.392698764801025 , 3.14159011840820 )= 9.701712503337716E-007 i= 3 , ub( 0.785397529602051 , 3.14159011840820 )= 1.792642957736665E-006 i= 4 , ub( 1.17809629440308 , 3.14159011840820 )= 2.342201459965859E-006 i= 5 , ub( 1.57079505920410 , 3.14159011840820 )= 2.535181590108706E-006 i= 6 , ub( 1.96349382400513 , 3.14159011840820 )= 2.342203919526153E-006 i= 7 , ub( 2.35619258880615 , 3.14159011840820 )= 1.792647502412089E-006 i= 8 , ub( 2.74889135360718 , 3.14159011840820 )= 9.701771882397932E-007 i= 9 , ub( 3.14159011840820 , 3.14159011840820 )= 6.427145694836435E-012 y grid and analytic solution, at xmax ii= 1 , ub( 3.14159011840820 , 0.00000000000000 )= 0.00000000000000 ii= 2 , ub( 3.14159011840820 , 0.392698764801025 )= 9.701712503337716E-007 ii= 3 , ub( 3.14159011840820 , 0.785397529602051 )= 1.792642957736665E-006 ii= 4 , ub( 3.14159011840820 , 1.17809629440308 )= 2.342201459965860E-006 ii= 5 , ub( 3.14159011840820 , 1.57079505920410 )= 2.535181590108706E-006 ii= 6 , ub( 3.14159011840820 , 1.96349382400513 )= 2.342203919526153E-006 ii= 7 , ub( 3.14159011840820 , 2.35619258880615 )= 1.792647502412089E-006 ii= 8 , ub( 3.14159011840820 , 2.74889135360718 )= 9.701771882397932E-007 ii= 9 , ub( 3.14159011840820 , 3.14159011840820 )= 6.427145694836435E-012 calling gaulegf npx= 9 calling gaulegf npy= 9 xx(1)= 5.001373846766290E-002 , xx(2)= 0.257561526474488 , wx(1)= 0.127665407678188 , wx(2)= 0.283761238273791 yy(1)= 5.001373846766290E-002 , yy(2)= 0.257561526474488 , wy(1)= 0.127665407678188 , wy(2)= 0.283761238273791 galk(xx(2),yy(2),2,2,2,2)= -7392.78467335411 galf(xx(2),yy(2),2,2)= 0.570906889281945 time to initialize = 1.0000000E-03 seconds compute stiffness matrix k computed stiffness matrix, see above f computed forcing function, see above time for stiffness and forcing = 194.3180 seconds time to solve equations = 6.0000001E-03 seconds iostat= 0 writing fem_bihar2dps_la_f90.dat finished writing fem_bihar2dps_la_f90.dat check_soln values maxerr= NaN , rmserr= NaN , avgerr= NaN time write and check solution = 2.0000001E-03 seconds ug computed Galerkin, Ua analytic, error ug(1,1)= 0.0000, Ua= 0.0000, err= -0.1505183E-12 ug(1,2)= 0.0000, Ua= 0.0000, err= 0.1136452E-13 ug(1,3)= 0.0000, Ua= 0.0000, err= 0.2528360E-12 ug(1,4)= 0.0000, Ua= 0.0000, err= -0.1851179E-17 ug(1,5)= 0.0000, Ua= 0.0000, err= -0.7606235E-13 ug(1,6)= 0.0000, Ua= 0.0000, err= 0.7487833E-20 ug(1,7)= 0.0000, Ua= 0.0000, err= 0.1655809E-12 ug(1,8)= 0.0000, Ua= 0.0000, err= -0.7316307E-14 ug(1,9)= 0.0000, Ua= 0.0000, err= 0.6910807E-12 ug(2,1)= 0.0000, Ua= 0.0000, err= 0.1659179E-12 ug(2,2)= 0.0925, Ua= 0.1464, err= -0.5399416E-01 ug(2,3)= 0.1808, Ua= 0.2706, err= -0.8978697E-01 ug(2,4)= 0.2430, Ua= 0.3536, err= -0.1105780E+00 ug(2,5)= 0.2652, Ua= 0.3827, err= -0.1174355E+00 ug(2,6)= 0.2430, Ua= 0.3536, err= -0.1105780E+00 ug(2,7)= 0.1808, Ua= 0.2706, err= -0.8978692E-01 ug(2,8)= 0.0925, Ua= 0.1464, err= -0.5399412E-01 ug(2,9)= 0.0000, Ua= 0.0000, err= -0.1873419E-14 ug(3,1)= 0.0000, Ua= 0.0000, err= -0.5933272E-15 ug(3,2)= 0.1808, Ua= 0.2706, err= -0.8978697E-01 ug(3,3)= 0.3525, Ua= 0.5000, err= -0.1474603E+00 ug(3,4)= 0.4731, Ua= 0.6533, err= -0.1802216E+00 ug(3,5)= 0.5162, Ua= 0.7071, err= -0.1909064E+00 ug(3,6)= 0.4731, Ua= 0.6533, err= -0.1802215E+00 ug(3,7)= 0.3525, Ua= 0.5000, err= -0.1474602E+00 ug(3,8)= 0.1808, Ua= 0.2706, err= -0.8978689E-01 ug(3,9)= 0.0000, Ua= 0.0000, err= -0.3103323E-15 ug(4,1)= 0.0000, Ua= 0.0000, err= -0.1641451E-13 ug(4,2)= 0.2430, Ua= 0.3536, err= -0.1105780E+00 ug(4,3)= 0.4731, Ua= 0.6533, err= -0.1802216E+00 ug(4,4)= 0.6343, Ua= 0.8536, err= -0.2192105E+00 ug(4,5)= 0.6920, Ua= 0.9239, err= -0.2318310E+00 ug(4,6)= 0.6343, Ua= 0.8536, err= -0.2192104E+00 ug(4,7)= 0.4731, Ua= 0.6533, err= -0.1802215E+00 ug(4,8)= 0.2430, Ua= 0.3536, err= -0.1105779E+00 ug(4,9)= 0.0000, Ua= 0.0000, err= 0.1755630E-13 ug(5,1)= 0.0000, Ua= 0.0000, err= -0.1696801E-20 ug(5,2)= 0.2652, Ua= 0.3827, err= -0.1174355E+00 ug(5,3)= 0.5162, Ua= 0.7071, err= -0.1909064E+00 ug(5,4)= 0.6920, Ua= 0.9239, err= -0.2318310E+00 ug(5,5)= 0.7550, Ua= 1.0000, err= -0.2450429E+00 ug(5,6)= 0.6920, Ua= 0.9239, err= -0.2318309E+00 ug(5,7)= 0.5162, Ua= 0.7071, err= -0.1909063E+00 ug(5,8)= 0.2653, Ua= 0.3827, err= -0.1174354E+00 ug(5,9)= 0.0000, Ua= 0.0000, err= -0.2202115E-14 ug(6,1)= 0.0000, Ua= 0.0000, err= -0.4196451E-14 ug(6,2)= 0.2430, Ua= 0.3536, err= -0.1105780E+00 ug(6,3)= 0.4731, Ua= 0.6533, err= -0.1802215E+00 ug(6,4)= 0.6343, Ua= 0.8536, err= -0.2192104E+00 ug(6,5)= 0.6920, Ua= 0.9239, err= -0.2318309E+00 ug(6,6)= 0.6343, Ua= 0.8536, err= -0.2192104E+00 ug(6,7)= 0.4731, Ua= 0.6533, err= -0.1802214E+00 ug(6,8)= 0.2430, Ua= 0.3536, err= -0.1105779E+00 ug(6,9)= 0.0000, Ua= 0.0000, err= 0.5145725E-18 ug(7,1)= 0.0000, Ua= 0.0000, err= -0.6048301E-15 ug(7,2)= 0.1808, Ua= 0.2706, err= -0.8978692E-01 ug(7,3)= 0.3525, Ua= 0.5000, err= -0.1474602E+00 ug(7,4)= 0.4731, Ua= 0.6533, err= -0.1802215E+00 ug(7,5)= 0.5162, Ua= 0.7071, err= -0.1909063E+00 ug(7,6)= 0.4731, Ua= 0.6533, err= -0.1802214E+00 ug(7,7)= 0.3525, Ua= 0.5000, err= -0.1474601E+00 ug(7,8)= 0.1808, Ua= 0.2706, err= -0.8978685E-01 ug(7,9)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(8,1)= 0.0000, Ua= 0.0000, err= -0.2979707E-15 ug(8,2)= 0.0925, Ua= 0.1464, err= -0.5399412E-01 ug(8,3)= 0.1808, Ua= 0.2706, err= -0.8978689E-01 ug(8,4)= 0.2430, Ua= 0.3536, err= -0.1105779E+00 ug(8,5)= 0.2653, Ua= 0.3827, err= -0.1174354E+00 ug(8,6)= 0.2430, Ua= 0.3536, err= -0.1105779E+00 ug(8,7)= 0.1808, Ua= 0.2706, err= -0.8978685E-01 ug(8,8)= 0.0925, Ua= 0.1464, err= -0.5399408E-01 ug(8,9)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,1)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,2)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,3)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,4)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,5)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,6)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,7)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,8)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 ug(9,9)= 0.0000, Ua= 0.0000, err= 0.0000000E+00 maxerr= 0.245042893940318 , avgerr= 8.806276801078400E-002 xmax= 3.14159011840820 , ymax= 3.14159011840820 , nx= 9 , ny= 9 , npx= 9 , npy= 9 total wall time = 194.3280 seconds end fem_bihar2dps_la.f90