Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
HTML articles powered by AMS MathViewer

by Natalia Kopteva PDF
Math. Comp. 76 (2007), 631-646 Request permission


A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter $\varepsilon ^2$ is arbitrarily small, which induces boundary layers. Constructing discrete sub- and super-solutions, we prove existence and investigate the accuracy of multiple discrete solutions on layer-adapted meshes of Bakhvalov and Shishkin types. It is shown that one gets second-order convergence (with, in the case of the Shishkin mesh, a logarithmic factor) in the discrete maximum norm, uniformly in $\varepsilon$ for $\varepsilon \le Ch$. Here $h>0$ is the maximum side length of mesh elements, while the number of mesh nodes does not exceed $Ch^{-2}$. Numerical experiments are performed to support the theoretical results.
Similar Articles
Additional Information
  • Natalia Kopteva
  • Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
  • MR Author ID: 610720
  • ORCID: 0000-0001-7477-6926
  • Email:
  • Received by editor(s): October 8, 2005
  • Received by editor(s) in revised form: February 23, 2006
  • Published electronically: December 27, 2006
  • Additional Notes: This publication has emanated from research conducted with the financial support of Science Foundation Ireland under the Basic Research Grant Programme 2004; Grant 04/BR/M0055.

  • Dedicated: Dedicated to Professor V. B. Andreev on the occasion of his 65th birthday
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 631-646
  • MSC (2000): Primary 65N06, 65N15, 65N30; Secondary 35B25
  • DOI:
  • MathSciNet review: 2291831