A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
1 Centre de Recerca Matemàtica, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain.
2 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.
3 Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria.
4 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
Received: 25 October 2011
Revised: 3 September 2012
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.
Mathematics Subject Classification: 65F10 / 65N20 / 65N30
Key words: Linear elasticity equations / locking free discretizations / preconditioning
© EDP Sciences, SMAI, 2013