Finite elements scheme in enriched subspaces for singularly perturbed reaction-diffusion problems on a square domain
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- Finite elements scheme in enriched subspaces for singularly perturbed reaction-diffusion problems on a square domain
- Jung, Chang-Yeol
- Issue Date
- IOS PRESS
- ASYMPTOTIC ANALYSIS, v.57, no.1-2, pp.41 - 69
- In this article, we discuss reaction-diffusion problems which produce ordinary boundary layers and elliptic corner layers. Using the classical polynomial Q1-finite elements spaces enriched with the so-called boundary layer elements which absorb the singularities due to the boundary and corner layers we are able to attain high numerical accuracies. We essentially obtain ε-uniform approximation errors in a weighted energy norm with significant simplifications in the numerical implementations; here we do not use mesh refinements.
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