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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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A posteriori error estimates for Maxwell equations
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by Joachim Schöberl PDF
Math. Comp. 77 (2008), 633-649 Request permission

Abstract:

Maxwell equations are posed as variational boundary value problems in the function space $H(\operatorname {curl})$ and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish new error estimates for the commuting quasi-interpolation operators recently introduced in J. Schöberl, Commuting quasi-interpolation operators for mixed finite elements. Similar estimates are required for additive Schwarz preconditioning. To incorporate boundary conditions, we establish a new extension result.
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Additional Information
  • Joachim Schöberl
  • Affiliation: Center for Computational Engineering Science, RWTH Aachen University, Pauwelstrasse 19, D-52074 Aachen, Germany
  • Received by editor(s): May 5, 2005
  • Received by editor(s) in revised form: July 25, 2006
  • Published electronically: December 12, 2007
  • Additional Notes: The author acknowledges support from the Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austria, and from the Austrian Science Foundation FWF within project grant Start Y-192, “hp-FEM: Fast Solvers and Adaptivity”
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 633-649
  • MSC (2000): Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-07-02030-3
  • MathSciNet review: 2373173