Objectives 1. Verify the provided m-file template for the linear basis FE implementation of GWSh for 2-D steady heat transport, i.e., the Peclet problem. Then edit this m-file template to implement the steady TWSh FE algorithm assuming all meshes used will be uniform, which simplifies the data specification of mesh measure h. h. 2. Perform a mesh refinement study for the GWSh and TWSh FE algorithms for Pe = 10 on M = 10x10, 20x20, 40x40, etc., uniform meshes, hence determine the minimum M required to produce a monotone solution. Make sure to adjust the position of the fixed Dirichet BC node for each M specification. Use these data to estimate each algorithm asymptotic convergence rate in the energy norm using log scales. 3. Repeat the Objective 2 mesh refinement study for both FE algorithms for Pe = 1000 on M = 10x10, 20x20, 40x40, 80x80 and 160x160 uniform meshes. For the TWSh FE solution data, graph in log scale hence verfy the theory predicted 4th order asymptotic convergence rate in the energy norm. This analysis cannot be done for the GWSh algorithm as the solutions are never monotone, hence dominated by "false energy." |