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Interior penalty method for the indefinite time-harmonic Maxwell equations

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Summary

In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order (hmin{s,ℓ}) with respect to the mesh size h, the polynomial degree ℓ, and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order (hℓ+1). The theoretical results are confirmed in a series of numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics, University of Leicester, Leicester, LE1 7RH, England

    Paul Houston

  2. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Ilaria Perugia

  3. Department of Mathematics, University of Basel, Rheinsprung 21, 4051, Basel, Switzerland

    Anna Schneebeli

  4. Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver, V6T 1Z2, Canada

    Dominik Schötzau

Authors
  1. Paul Houston
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  2. Ilaria Perugia
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  3. Anna Schneebeli
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  4. Dominik Schötzau
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Corresponding author

Correspondence to Paul Houston.

Additional information

Supported by the EPSRC (Grant GR/R76615).

Supported by the Swiss National Science Foundation under project 21-068126.02.

Supported in part by the Natural Sciences and Engineering Council of Canada.

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Houston, P., Perugia, I., Schneebeli, A. et al. Interior penalty method for the indefinite time-harmonic Maxwell equations. Numer. Math. 100, 485–518 (2005). https://doi.org/10.1007/s00211-005-0604-7

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  • DOI: https://doi.org/10.1007/s00211-005-0604-7

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