FEM2D_BVP_LINEAR Python version 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 0.000000 0.000000 0.250000 0.000000 0.500000 0.000000 0.750000 0.000000 1.000000 0.000000 0.000000 0.250000 0.250000 0.250000 0.500000 0.250000 0.750000 0.250000 1.000000 0.250000 0.000000 0.500000 0.250000 0.500000 0.500000 0.500000 0.750000 0.500000 1.000000 0.500000 0.000000 0.750000 0.250000 0.750000 0.500000 0.750000 0.750000 0.750000 1.000000 0.750000 0.000000 1.000000 0.250000 1.000000 0.500000 1.000000 0.750000 1.000000 1.000000 1.000000 0 1 6 5 1 2 7 6 2 3 8 7 3 4 9 8 5 6 11 10 6 7 12 11 7 8 13 12 8 9 14 13 10 11 16 15 11 12 17 16 12 13 18 17 13 14 19 18 15 16 21 20 16 17 22 21 17 18 23 22 18 19 24 23 FEM2D_BVP_LINEAR: Normal end of execution.