A stable mixed finite element method for nearly incompressible linear elastostatics

We present a new, stable, mixed finite element (FE) method for linear elastostatics of nearly incompressible solids. The is the automatic variationally stable FE (AVS-FE) Calo, Romkes and Valseth, in which we consider Petrov-Galerkin weak formulation where stress displacement variables are space H(div)xH1, respectively. This allows us to employ fully conforming discretization any elastic solid using classical subspaces H(div) H1. Hence, resulting approximation yields both continuous stresses displacements. To ensure stability method, philosophy discontinuous (DPG) Demkowicz Gopalakrishnan use optimal test spaces. Thus, even as Poisson ratio approaches 0.5, system algebraic equations symmetric positive definite. Our also comes with built-in posteriori error estimator well indicators used drive mesh adaptive refinements. several numerical verifications our including comparisons existing technologies.