A posteriori error analysis for the mixed Laplace eigenvalue problem

Abstract: This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem with homogeneous Dirichlet boundary conditions. In particular, the resulting error estimator constitutes an upper bound for the error and is shown to be local efficient. Therefore, we present a reconstruction in the standard $H^1_0$-conforming space for the primal variable of the mixed Laplace eigenvalue problem. This reconstruction is performed locally on a set of vertex patches.