Tue Oct 19 11:34:32 2021 fem2d_bvp_linear_test Python version: 3.6.9 Given the boundary value problem on the unit square: - uxx - uyy = x, 0 < x < 1, 0 < y < 1 with boundary conditions u(0,y) = u(1,y) = u(x,0) = u(x,1) = 0, demonstrate how the finite element method can be used to define and compute a discrete approximation to the solution. This program uses quadrilateral elements and piecewise continuous bilinear basis functions. Nodes along X axis: 0 0.000000 1 0.250000 2 0.500000 3 0.750000 4 1.000000 I J V X Y U Uexact 0 0 0 0.000000 0.000000 0 0 1 0 1 0.250000 0.000000 0 0 2 0 2 0.500000 0.000000 0 0 3 0 3 0.750000 0.000000 0 0 4 0 4 1.000000 0.000000 0 0 0 1 5 0.000000 0.250000 0 0 1 1 6 0.250000 0.250000 0.0371652 0.0351562 2 1 7 0.500000 0.250000 0.0493862 0.046875 3 1 8 0.750000 0.250000 0.0371652 0.0351562 4 1 9 1.000000 0.250000 0 0 0 2 10 0.000000 0.500000 0 0 1 2 11 0.250000 0.500000 0.0493862 0.046875 2 2 12 0.500000 0.500000 0.0657366 0.0625 3 2 13 0.750000 0.500000 0.0493862 0.046875 4 2 14 1.000000 0.500000 0 0 0 3 15 0.000000 0.750000 0 0 1 3 16 0.250000 0.750000 0.0371652 0.0351562 2 3 17 0.500000 0.750000 0.0493862 0.046875 3 3 18 0.750000 0.750000 0.0371652 0.0351562 4 3 19 1.000000 0.750000 0 0 0 4 20 0.000000 1.000000 0 0 1 4 21 0.250000 1.000000 0 0 2 4 22 0.500000 1.000000 0 0 3 4 23 0.750000 1.000000 0 0 4 4 24 1.000000 1.000000 0 0 fem2d_bvp_linear_test: Normal end of execution. Tue Oct 19 11:34:32 2021