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An Adaptive P 1 Finite Element Method for Two-Dimensional Maxwell’s Equations

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Abstract

Recently a new numerical approach for two-dimensional Maxwell’s equations based on the Hodge decomposition for divergence-free vector fields was introduced by Brenner et al. In this paper we present an adaptive P 1 finite element method for two-dimensional Maxwell’s equations that is based on this new approach. The reliability and efficiency of a posteriori error estimators based on the residual and the dual weighted-residual are verified numerically. The performance of the new approach is shown to be competitive with the lowest order edge element of Nédélec’s first family.

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Acknowledgements

The bulk of this paper was written while the second author enjoyed the hospitality of the Center for Computation and Technology at Louisiana State University.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation & Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    S. C. Brenner & L.-Y. Sung

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    J. Gedicke

Authors
  1. S. C. Brenner
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  2. J. Gedicke
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  3. L.-Y. Sung
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Corresponding author

Correspondence to S. C. Brenner.

Additional information

This work was supported in part by the National Science Foundation under Grant No. DMS-07-13835 and Grand No. DMS-10-16332. The second author was additionally supported by the DFG Research Center MATHEON “Mathematics for Key Technologies” and the DFG graduate school BMS “Berlin Mathematical School”.

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Brenner, S.C., Gedicke, J. & Sung, LY. An Adaptive P 1 Finite Element Method for Two-Dimensional Maxwell’s Equations. J Sci Comput 55, 738–754 (2013). https://doi.org/10.1007/s10915-012-9658-8

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  • DOI: https://doi.org/10.1007/s10915-012-9658-8

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