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.
@article{M2AN_2013__47_5_1315_0,
author = {Ayuso de Dios, Blanca and Georgiev, Ivan and Kraus, Johannes and Zikatanov, Ludmil},
title = {A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {1315-1333},
doi = {10.1051/m2an/2013070},
mrnumber = {3100765},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_5_1315_0}
}
Ayuso de Dios, Blanca; Georgiev, Ivan; Kraus, Johannes; Zikatanov, Ludmil. A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 1315-1333. doi : 10.1051/m2an/2013070. http://gdmltest.u-ga.fr/item/M2AN_2013__47_5_1315_0/
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