Uniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem
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- by Dmitriy Leykekhman PDF
- Math. Comp. 77 (2008), 21-39 Request permission
Abstract:
Consider the problem $-\epsilon ^2\Delta u+u=f$ with homogeneous Neumann boundary condition in a bounded smooth domain in $\mathbb {R}^N$. The whole range $0<\epsilon \le 1$ is treated. The Galerkin finite element method is used on a globally quasi-uniform mesh of size $h$; the mesh is fixed and independent of $\epsilon$. A precise analysis of how the error at each point depends on $h$ and $\epsilon$ is presented. As an application, first order error estimates in $h$, which are uniform with respect to $\epsilon$, are given.References
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Additional Information
- Dmitriy Leykekhman
- Affiliation: Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005
- MR Author ID: 680657
- Email: dmitriy@caam.rice.edu
- Received by editor(s): June 8, 2005
- Received by editor(s) in revised form: November 18, 2006
- Published electronically: May 14, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 21-39
- MSC (2000): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-07-02015-7
- MathSciNet review: 2353942