Asymptotically Exact A Posteriori Error Analysis for the Mixed Laplace Eigenvalue Problem

This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem. We discuss a reconstruction in the standard H₀¹-conforming space for the primal variable of the mixed Laplace eigenvalue problem and compare it with analogous approaches present in the literature for the corresponding source problem. In the case of Raviart–Thomas finite elements of arbitrary polynomial degree, the resulting error estimator constitutes a guaranteed upper bound for the error and is shown to be local efficient. Our reconstruction is performed locally on a set of vertex patches.