Residual-baseda posteriorierror estimation for the Maxwell’s eigenvalue problem

Abstract

We present an a posteriori estimator of the error in the L 2 -norm for the numerical approximation of the Maxwell's eigenvalue problem by means of N ed elec nite elements (see, for instance, (4)). As in (2), our analysis is based on a Helmholtz decomposition of the error, where, in particular, the L 2 -orthogonality property is used to derive a superconvergence result for the eigenfunction approximation. The analysis also makes use of a priori error estimates and the additional regularity of the eigenfunctions (see (3)). Inspired by (1), we prove a key result about superconvergence between the L 2 -orthogonal projection of the exact eigenfunction onto the curl of the N ed elec space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms. Finally, the eciency of the error indicators is shown by using a standard bubble functions technique.