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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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


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.
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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:
  • Natalia Kopteva
  • Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
  • Email:
  • 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:
  • MathSciNet review: 2429877