Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems

Abstract We derive optimal and asymptotically exact a posteriori error estimates for the approximation of eigenfunction Laplace eigenvalue problem. To do so, we combine two results from literature. First, use hypercircle techniques developed mixed approximations with Raviart-Thomas finite elements. In addition, post-processings introduced based on Brezzi-Douglas-Marini element. these approaches, define novel additional local post-processing fluxes that appropriately modifies divergence without compromising properties. Consequently, new flux can be used to upper bounds eigenfunction, corresponding eigenvalue. Numerical examples validate theory motivate an adaptive mesh refinement.