Daniele Boffi, Lucia Gastaldi, Rodolfo Rodríguez, Ivana Sebestova:
Residual-based a posteriori error estimation for the Maxwell eigenvalue problem
We present an a posteriori estimator of the error in the L2-norm for the numerical approximation of the Maxwell eigenvalue problem by means of Nedelec finite elements. Our analysis is based on a Helmholtz decomposition of the error and on a superconvergence result between the L2-orthogonal projection of the exact eigenfunction onto the curl of the Nedelec finite element space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms and local efficiency of the error indicators is shown by using a standard bubble functions technique. The behavior of the a posteriori error estimator is illustrated on a numerical test.