no. 5
A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 5, pp. 1315-1333.

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.

DOI : 10.1051/m2an/2013070
Classification : 65F10, 65N20, 65N30
Mots clés : linear elasticity equations, locking free discretizations, preconditioning 
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     title = {A subspace correction method for discontinuous {Galerkin} discretizations of linear elasticity equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1315--1333},
     publisher = {EDP-Sciences},
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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 , Tome 47 (2013) no. 5, pp. 1315-1333. doi : 10.1051/m2an/2013070. http://archive.numdam.org/articles/10.1051/m2an/2013070/

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