FEM1D_BVP_QUADRATIC Python version Given the two point boundary value problem: -u'' = x * ( x + 3 ) * exp ( x ), 0 < x < 1 with boundary conditions u(0) = 0, u(1) = 0, demonstrate how the finite element method can be used to define and compute a discrete approximation to the solution. This program uses piecewise quadratic elements. Nodes: 0 0.000000 1 0.100000 2 0.200000 3 0.300000 4 0.400000 5 0.500000 6 0.600000 7 0.700000 8 0.800000 9 0.900000 10 1.000000 RHS 0 0.000000 1 0.046966 2 0.050563 3 0.180018 4 0.133062 5 0.387288 6 0.259311 7 0.699015 8 0.446788 9 1.156055 10 0.000000 Node Ucomp Uexact Error 0 -1.9984e-15 0 1.9984e-15 1 0.0994734 0.0994654 8.05308e-06 2 0.195424 0.195424 1.06371e-09 3 0.283482 0.28347 1.1505e-05 4 0.358038 0.358038 1.73068e-09 5 0.412197 0.41218 1.62001e-05 6 0.437309 0.437309 1.88347e-09 7 0.422911 0.422888 2.25438e-05 8 0.356087 0.356087 1.37113e-09 9 0.221395 0.221364 3.10661e-05 10 0 0 0 FEM1D_BVP_QUADRATIC: Normal end of execution.