Uniform preconditioners for high order finite element approximations of planar linear elasticity

Abstract

A new overlapping Additive Schwarz preconditioner is developed for high order finite element approximation of planar linear elastic problems on triangular meshes. The new preconditioner results in a condition number that isbounded independently of the degreepp, the mesh-sizehhand the ratioλ/μ\lambda /\mu. The resulting condition number is reduced to roughly6.06.0for all values of the parameters and discretization parameters on standard test problems. Crucially, the overall cost of the new preconditioner is comparable to the cost of applying standard domain decomposition based preconditioners.