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

TL;DR

This paper introduces subspace correction preconditioning techniques for discontinuous Galerkin discretizations of linear elasticity equations, providing optimal convergence analysis and numerical validation for various boundary conditions.

Contribution

It proposes a novel subspace correction method tailored for DG discretizations of linear elasticity, with proven optimality and comprehensive analysis.

Findings

Preconditioners are optimal with respect to mesh size and material parameters.

Numerical results confirm theoretical convergence and efficiency.

Method applies to pure displacement, mixed, and traction-free problems.

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 Lame 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.