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

Title: A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems
Creator: Lamichhane, Bishnu P.; McBride, A. T.; Reddy, B. D.
Relation: Computer Methods in Applied Mechanics and Engineering Vol. 258, p. 109-117
Publisher Link: http://dx.doi.org/10.1016/j.cma.2013.02.008
Publisher: Elsevier
Resource Type: journal article
Date: 2013
Description: 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.
Subject: elasticity; three-field formulation; biorthogonal system; mixed finite elements; a priori estimate
Identifier: http://hdl.handle.net/1959.13/1300924
Identifier: uon:20185
Identifier: ISSN:0045-7825
Language: eng
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