Comparison of the Two-grid Method on Different Meshes for Singularly Perturbed Semilinear Problems.

A two-grid algorithm for FEM solution of nonlinear reaction diffusion equations was constructed. The algorithm involves solving one small, nonlinear problem on the coarse-grid system, one-linear problem on the fine-grid system. Three meshes (Shishkin’s, Bakhvalov’s and Vulanovic’s) are examined. All of the approximations are uniformly convergent with respect to the small parameter. We prove that when the mesh step parameters are chosen appropriately, the error in the two-grid algorithm is comparable to the error in solving the fully nonlinear problem on the fine mesh. We also provide an analysis of numerical experiments. [ABSTRACT FROM AUTHOR]