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A posteriori error analysis for the mixed Laplace eigenvalue problem: investigations for the BDM‐element
Author(s) -
Bertrand Fleurianne,
Boffi Daniele,
Stenberg Rolf
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900155
Subject(s) - estimator , mathematics , eigenvalues and eigenvectors , finite element method , degree of a polynomial , a priori and a posteriori , laplace transform , extension (predicate logic) , polynomial , variable (mathematics) , mixed finite element method , mathematical optimization , mathematical analysis , statistics , computer science , philosophy , physics , epistemology , quantum mechanics , thermodynamics , programming language
A posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem can be derived using a reconstruction in the standard H 0 1 ‐conforming space for the primal variable of the mixed 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. This paper shows that the extension for the BDM‐element is not straightforward.