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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 2024 MCQ for Mathematics of Computation is 1.78.

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Sharp estimates for finite element approximations to elliptic problems with Neumann boundary data of low regularity
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by Aaron Solo;
Math. Comp. 76 (2007), 1787-1800
DOI: https://doi.org/10.1090/S0025-5718-07-01993-X
Published electronically: May 3, 2007

Abstract:

Consider a second order homogeneous elliptic problem with smooth coefficients, $Au = 0$, on a smooth domain, $\Omega$, but with Neumann boundary data of low regularity. Interior maximum norm error estimates are given for $C^0$ finite element approximations to this problem. When the Neumann data is not in $L^1(\partial \Omega )$, these local estimates are not of optimal order but are nevertheless shown to be sharp. A method for ameliorating this sub-optimality by preliminary smoothing of the boundary data is given. Numerical examples illustrate the findings.
References
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Bibliographic Information
  • Aaron Solo
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • Address at time of publication: Susquehanna International Group, 401 City Line Avenue, Bala Cynwyd, Pennsylvania 19004
  • Email: als54@cornell.edu
  • Received by editor(s): April 11, 2006
  • Received by editor(s) in revised form: August 2, 2006
  • Published electronically: May 3, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1787-1800
  • MSC (2000): Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-07-01993-X
  • MathSciNet review: 2336268