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The mortar-discontinuous Galerkin method for the 2D Maxwell eigenproblem. (English) Zbl 1203.65246

Summary: 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.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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