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

  • Gang Chen and Xiaoping Xie EMAIL logo

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.

MSC 2010: 65N30

Award Identifier / Grant number: 11171239

Award Identifier / Grant number: 91430105

Funding statement: 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.

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Received: 2015-10-6
Revised: 2016-2-25
Accepted: 2016-2-29
Published Online: 2016-3-10
Published in Print: 2016-7-1

© 2016 by De Gruyter

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