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The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem

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Abstract

We consider discontinuous Galerkin (DG) approximations of the Maxwell eigenproblem on meshes with hanging nodes. It is known that while standard DG methods provide spurious-free and accurate approximations on the so-called k-irregular meshes, they may generate spurious solutions on general irregular meshes. In this paper we present a mortar-type method to cure this problem in the two-dimensional case. More precisely, we introduce a projection based penalization at non-conforming interfaces and prove that the obtained DG methods are spectrally correct. The theoretical results are validated in a series of numerical experiments on both convex and non convex problem domains, and with both regular and discontinuous material coefficients.

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Authors and Affiliations

  1. Istituto di Matematica Applicata e Tecnologie Informatiche–CNR, Via Ferrata 1, 27100, Pavia, Italy

    Annalisa Buffa

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

    Ilaria Perugia

  3. Department of Computational and Applies Mathematics, Rice University, 6100 Main Street–MS 134, Houston, TX, 77005-1892, USA

    Tim Warburton

Authors
  1. Annalisa Buffa
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  2. Ilaria Perugia
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  3. Tim Warburton
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Correspondence to Ilaria Perugia.

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Buffa, A., Perugia, I. & Warburton, T. The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem. J Sci Comput 40, 86–114 (2009). https://doi.org/10.1007/s10915-008-9238-0

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  • DOI: https://doi.org/10.1007/s10915-008-9238-0

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