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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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Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements
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by Zhiqiang Cai, Cuiyu He and Shun Zhang PDF
Math. Comp. 86 (2017), 617-636 Request permission

Abstract:

In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach without using the Helmholtz decomposition. It is proved that the estimator is reliable with constant independent of the jump of diffusion coefficients across the interfaces, without the assumption that the diffusion coefficient is quasi-monotone. Numerical results for one test problem with intersecting interfaces are also presented.
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Additional Information
  • Zhiqiang Cai
  • Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
  • MR Author ID: 235961
  • Email: caiz@purdue.edu
  • Cuiyu He
  • Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
  • Email: he75@purdue.edu
  • Shun Zhang
  • Affiliation: Department of Mathematics, City University of Hong Kong, Hong Kong
  • MR Author ID: 704861
  • Email: shun.zhang@cityu.edu.hk
  • Received by editor(s): July 17, 2014
  • Received by editor(s) in revised form: September 9, 2015
  • Published electronically: May 3, 2016
  • Additional Notes: This work was supported in part by the National Science Foundation under grants DMS-1217081 and DMS-1522707, the Purdue Research Foundation, and the Research Grants Council of the Hong Kong SAR, China, under the GRF Project No. 11303914, CityU 9042090.
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 617-636
  • MSC (2010): Primary 65N30
  • DOI: https://doi.org/10.1090/mcom/3151
  • MathSciNet review: 3584542