Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh
Date
2003ISSN
0749-159XSource
Numerical Methods for Partial Differential EquationsVolume
19Issue
1Pages
89-111Google Scholar check
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We consider the numerical approximation of singularly perturbed reaction-diffusion problems over two-dimensional domains with smooth boundary. Using the h version of the finite element method over appropriately designed piecewise uniform (Shishkin) meshes, we are able to uniformly approximate the solution at a quasi-optimal rate. The results of numerical computations showing agreement with the analysis are also presented.