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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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