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A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

Published online by Cambridge University Press:  09 July 2013

Blanca Ayuso de Dios ,
Ivan Georgiev ,
Johannes Kraus  and
Ludmil Zikatanov
Blanca Ayuso de Dios
Affiliation:
Centre de Recerca Matemàtica, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain.. bayuso@crm.cat
Ivan Georgiev
Affiliation:
Institue of Mathematics and Informatics, Bulgarian Academy of Sciences and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria.; ivan.georgiev@oeaw.ac.at
Johannes Kraus
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria.; johannes.kraus@oeaw.ac.at
Ludmil Zikatanov
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.; ltz@math.psu.edu
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Abstract

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

Keywords

Linear elasticity equationslocking free discretizationspreconditioning
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1315 - 1333
Copyright
© EDP Sciences, SMAI, 2013

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