A Two-Grid Method on Layer-Adapted Meshes for a Semilinear 2D Reaction-Diffusion Problem
A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discetizied by a two-grid scheme on layer-adapted meshes. In the first step, the nonlinear problem is discretized on coarse grid. In the second step, the problem is discretized on a fine grid and linearized around the interpolation of the computed solution on the first step. We show theoretically and numerically that the global error on Shishkin or Bakhvalov mesh is the same as would have been obtained if the nonlinear problem had been solved directly on the fine grid.
KeywordsCoarse Grid Singularly Perturb Shishkin Mesh Piecewise Linear Basis Function Singularly Perturb Problem
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