On the Finite Element Approximation of a 2D Maxwell Eigenvalue Problem in a Domain with Curved Boundaries

摘要

We consider a 2D Maxwell eigenvalue problem, arising from the modelling of electromagnetic resonances in cavities. This problem is recasted into an equivalent variational formulation in order to may establish a finite element approximation of the occurring electric and magnetic fields. A careful choice of the finite dimensional function space is crucial in order to exclude so-called spurious eigenmodes from the approximated spectrum.A triangulation of the domain is necessary, where we allow for both internal and external approximations of the domain. This gives rise to a triangulation error in the case where curved boundaries are present. In this paper we obtain convergence results when a triangulation error is committed. Necessary conditions to prevent the occurrence of spurious modes are proved.