Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh

✍ Scribed by Christos Xenophontos; Scott R. Fulton

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 678 KB
• Volume: 19
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.10034

✦ Synopsis

Abstract

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. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 89–111, 2003