A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations
We deal with the solution of the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The main focus of the paper is on constructing a uniform preconditioner which is based on a natural splitting of the space of piecewise linear discontinuous functions. The presented approach has recently been introduced in  in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
KeywordsLinear Elasticity Problem Interior Face Galerkin Discretizations Spectral Condition Number Discontinuous Galerkin Discretizations
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