Numerical PDE HW 9

Mesh refinement and convergence

Create a mesh refiner that takes in a 2D triangular mesh and splits every edge into 2.  Use this tool to generate a sequence of meshes for the square domain 0≤(Subscript[x, 1])≤1 and 0≤(Subscript[x, 2])≤1. Plot the coarsest and finest meshes you created and report the minimum/maximum  angles, minimum/maximum edge lengths, and the number of vertices for all your meshes.

Verify that the solution of the PDE (∂^({2,0}))u+(∂^({0,2}))u= Sin[π (Subscript[x, 1])/2]Cos[2π (Subscript[x, 2])]   with homogeneous Dirichlet conditions at (Subscript[x, 1])=0 and Homogeneous Neumann on the other sides is a multiple of  Sin[π (Subscript[x, 1])/2]Cos[2π (Subscript[x, 2])].  Show your computation and report the solution.

Verify that your solver produces appropriate convergence for the test problem in #2 for the meshes you created in #1.  Show labelled graphs of the errors measures discussed in Chpt 4 as function of h on appropriate scales.