An Adaptive Finite Element Scheme for the Hellinger–Reissner Elasticity Mixed Eigenvalue Problem-Reference-Cited by-同舟云学术

An Adaptive Finite Element Scheme for the Hellinger–Reissner Elasticity Mixed Eigenvalue Problem

Published:2021-02-02 Issue:0 Volume:0 Page:
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Bertrand Fleurianne¹^ORCID,Boffi Daniele²^ORCID,Ma Rui³^ORCID

Affiliation:

1. Faculty of Electrical Engineering, Mathematics and Computer Science , University of Twente , Zilverling, P.O. Box 217, 7500 AE Enschede , The Netherlands

2. Computer, Electrical and Mathematical Science and Engineering Division , 4700 King Abdullah University of Science and Technology , Thuwal 23955-6900 , Kingdom of Saudi Arabia ; and University of Pavia, Pavia, Italy

3. Fakultät für Mathematik , Universität Duisburg-Essen , Thea-Leymann-Straße 9, D-45127 Essen , Germany

Abstract

Abstract In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger–Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference18 articles.

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