Fast auxiliary space preconditioners for linear elasticity in mixed form

Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity

Abstract. Balancing Neumann-Neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coeÆcients, discretized with mixed nite or spectral elements with discontinuous pressures. These domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point S...

Balancing Neumann-Neumann Preconditioners for the Mixed Formulation of Almost-Incompressible Linear Elasticity

Balancing Neumann-Neumann methods are extended to the equations arising from the mixed formulation of almost-incompressible linear elasticity problems discretized with discontinuous-pressure finite elements. This family of domain decomposition algorithms has previously been shown to be effective for large finite element approximations of positive definite elliptic problems. Our methods are prov...

A Mixed Nonconforming Finite Element for Linear Elasticity

This article considers a mixed finite element method for linear elasticity. It is based on a modified mixed formulation that enforces the continuity of the stress weakly by adding a jump term of the approximated stress on interior edges. The symmetric stress are approximated by nonconforming linear elements and the displacement by piecewise constants. We establish (h) error bound in the (broken...

Symmetric Nonconforming Mixed Finite Elements for Linear Elasticity

We present a family of mixed methods for linear elasticity, that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces,...

Final Report on Subcontract B601287: Auxiliary Space Preconditioners and Algebraic Multilevel Solvers for Systems of PDEs