Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an $L$-shaped domain
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- by Vladimir B. Andreev and Natalia Kopteva PDF
- Math. Comp. 77 (2008), 2125-2139 Request permission
Abstract:
A singularly perturbed reaction-diffusion equation is posed in a two-dimensional $L$-shaped domain $\Omega$ subject to a continuous Dirchlet boundary condition. Its solutions are in the Hölder space $C^{2/3}(\bar \Omega )$ and typically exhibit boundary layers and corner singularities. The problem is discretized on a tensor-product Shishkin mesh that is further refined in a neighboorhood of the vertex of angle $3\pi /2$. We establish almost second-order convergence of our numerical method in the discrete maximum norm, uniformly in the small diffusion parameter. Numerical results are presented that support our theoretical error estimate.References
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Additional Information
- Vladimir B. Andreev
- Affiliation: Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, 119991, Moscow, Russia
- Email: andreev@cs.msu.su
- Natalia Kopteva
- Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
- Email: natalia.kopteva@ul.ie
- Received by editor(s): April 27, 2007
- Received by editor(s) in revised form: August 31, 2007
- Published electronically: February 19, 2008
- Additional Notes: This research was supported by Enterprise Ireland International Collaboration Programme grant IC/2006/8.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 2125-2139
- MSC (2000): Primary 65N06, 65N15, 65N50; Secondary 35B25
- DOI: https://doi.org/10.1090/S0025-5718-08-02106-6
- MathSciNet review: 2429877