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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr


IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

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1609-9389
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Volume 16, Issue 3

Issues

A Robust Weak Galerkin Finite Element Method for Linear Elasticity with Strong Symmetric Stresses

Gang Chen / Xiaoping Xie
Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/cmam-2016-0012

Abstract

This paper proposes and analyzes a weak Galerkin (WG) finite element method with strong symmetric stresses for two- and three-dimensional linear elasticity problems on conforming or nonconforming polygon/polyhedral meshes. The WG method uses piecewise-polynomial approximations of degrees k (1) for the stress, k+1 for the displacement, and k for the displacement trace on the inter-element boundaries. It is shown to be equivalent to a hybridizable discontinuous Galerkin (HDG) finite element scheme. We show that the WG methods are robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments confirm the theoretical results.

Keywords: Weak Galerkin Method; Linear Elasticity; Strong Symmetric Stress; Error Estimate

MSC 2010: 65N30

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About the article

Received: 2015-10-06

Revised: 2016-02-25

Accepted: 2016-02-29

Published Online: 2016-03-10

Published in Print: 2016-07-01


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11171239

Award identifier / Grant number: 91430105

This work was supported by the National Natural Science Foundation of China (11171239), by Major Research Plan of the National Natural Science Foundation of China (91430105), and by the Sino-German Science Center (grant 1228) on the occasion of the Chinese-German Workshop on Computational and Applied Mathematics in Augsburg 2015.


Citation Information: Computational Methods in Applied Mathematics, Volume 16, Issue 3, Pages 389–408, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2016-0012.

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