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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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Quasi-optimal and robust a posteriori error estimates in $L^\infty (L^2)$ for the approximation of Allen-Cahn equations past singularities
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by Sören Bartels and Rüdiger Müller PDF
Math. Comp. 80 (2011), 761-780 Request permission

Abstract:

Quasi-optimal a posteriori error estimates in $L^\infty (0,T;L^2(\Omega ))$ are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large class of conforming, nonconforming, mixed, and discontinuous Galerkin methods. Numerical experiments illustrate the theoretical results.
References
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Additional Information
  • Sören Bartels
  • Affiliation: Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstrasse 6, 53115 Bonn, Germany
  • Email: bartels@ins.uni-bonn.de
  • Rüdiger Müller
  • Affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
  • Email: mueller@wias-berlin.de
  • Received by editor(s): May 13, 2009
  • Received by editor(s) in revised form: February 1, 2010
  • Published electronically: November 18, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 761-780
  • MSC (2010): Primary 65M15, 65M50; Secondary 35K20
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02444-5
  • MathSciNet review: 2772095