A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems

Lamichhane, B. P., McBride, A. T. and Reddy, B. D. (2013) A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems. Computer Methods in Applied Mechanics and Engineering, 258, pp. 109-117. (doi:10.1016/j.cma.2013.02.008)

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Abstract

Abstract We consider a mixed finite element method based on simplicial triangulations for a three-field formulation of linear elasticity. The three-field formulation is based on three unknowns: displacement, stress and strain. In order to obtain an efficient discretization scheme, we use a pair of finite element bases forming a biorthogonal system for the strain and stress. The biorthogonality relation allows us to statically condense out the strain and stress from the saddle-point system leading to a symmetric and positive-definite system. The strain and stress can be recovered in a post-processing step simply by inverting a diagonal matrix. Moreover, we show a uniform convergence of the finite element approximation in the incompressible limit. Numerical experiments are presented to support the theoretical results.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Dr Andrew
Authors: Lamichhane, B. P., McBride, A. T., and Reddy, B. D.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138

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