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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations
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by Sangita Yadav, Amiya K. Pani and Eun-Jae Park
Math. Comp. 82 (2013), 1297-1335
DOI: https://doi.org/10.1090/S0025-5718-2013-02662-2
Published electronically: January 24, 2013

Abstract:

Based on the analysis of Cockburn et al. [Math. Comp. 78 (2009), pp. 1-24] for a selfadjoint linear elliptic equation, we first discuss superconvergence results for nonselfadjoint linear elliptic problems using discontinuous Galerkin methods. Further, we have extended our analysis to derive superconvergence results for quasilinear elliptic problems. When piecewise polynomials of degree $k\geq 1$ are used to approximate both the potential as well as the flux, it is shown, in this article, that the error estimate for the discrete flux in $L^2$-norm is of order $k+1.$ Further, based on solving a discrete linear elliptic problem at each element, a suitable postprocessing of the discrete potential is developed and then, it is proved that the resulting post-processed potential converges with order of convergence $k+2$ in $L^2$-norm. These results confirm superconvergent results for linear elliptic problems.
References
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Bibliographic Information
  • Sangita Yadav
  • Affiliation: Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076
  • Email: sangita@.iitk@gmail.com
  • Amiya K. Pani
  • Affiliation: Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076
  • Email: akp@math.iitb.ac.in
  • Eun-Jae Park
  • Affiliation: Department of Computational Science and Engineering-WCU, Yonsei University
  • Email: ejpark@yonsei.ac.kr
  • Received by editor(s): October 29, 2010
  • Received by editor(s) in revised form: November 15, 2011
  • Published electronically: January 24, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 82 (2013), 1297-1335
  • MSC (2010): Primary 65-XX
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02662-2
  • MathSciNet review: 3042565