Uniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem

Author:
Dmitriy Leykekhman

Journal:
Math. Comp. **77** (2008), 21-39

MSC (2000):
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-07-02015-7

Published electronically:
May 14, 2007

MathSciNet review:
2353942

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the problem with homogeneous Neumann boundary condition in a bounded smooth domain in . The whole range is treated. The Galerkin finite element method is used on a globally quasi-uniform mesh of size ; the mesh is fixed and independent of .

A precise analysis of how the error at each point depends on and is presented. As an application, first order error estimates in , which are uniform with respect to , are given.

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Additional Information

**Dmitriy Leykekhman**

Affiliation:
Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005

Email:
dmitriy@caam.rice.edu

DOI:
https://doi.org/10.1090/S0025-5718-07-02015-7

Keywords:
Finite element,
singularly perturbed,
pointwise estimates,
reaction-diffusion

Received by editor(s):
June 8, 2005

Received by editor(s) in revised form:
November 18, 2006

Published electronically:
May 14, 2007

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.