In this note we consider the a posteriori error analysis of mixed finite element approximations to the Laplace eigenvalue problem based on local postprocessing. The estimator makes use of an improved L2 approximation for the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) finite element methods. For the BDM method we also obtain improved eigenvalue convergence for postprocessed eigenvalues. We verify the theoretical results in several numerical examples.
Bibliographical noteKAUST Repository Item: Exported on 2022-01-11
Acknowledgements: Fleurianne Bertrand gratefully acknowledges support by the German Research Foundation (DFG) in the Priority Programme SPP 1748 Reliable simulation techniques in solid mechanics under grant number BE6511/1-1. Daniele Boffi is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR. Arbaz Khan has been supported by the faculty initiation grant MTD/FIG/100878 and Serb Matrics grant MTR/2020/000303.