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

Blanca Ayuso De Dios, Ivan Georgiev, Johannes Kraus, Ludmil Zikatanov

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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.

Original languageEnglish (US)
Pages (from-to)1315-1333
Number of pages19
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume47
Issue number5
DOIs
Publication statusPublished - Sep 1 2013

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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