The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem
- 194 Downloads
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.
KeywordsDiscontinuous Galerkin methods Maxwell’s equations Eigenvalue problems Mortar methods
Unable to display preview. Download preview PDF.
- 4.Bernardi, C., Maday, Y., Patera, A.T.: A new nonconforming approach to domain decomposition: The mortar elements method. In: Brezis, H., Lions, J.L. (eds.) Nonlinear Partial Differential Equations and Their Applications, pp. 13–51. Pitman, London (1994) Google Scholar
- 10.Dauge, M.: Benchmark computations for Maxwell equations for the approximation of highly singular solutions. http://perso.univ-rennes1.fr/monique.dauge/benchmax.html
- 16.Kato, T.: Perturbation Theory of Linear Operators. Springer, Berlin (1966) Google Scholar