Analysis and finite element approximation of compressible and incompressible linear isotropic elasticity based upon a variational principle

Abstract

We propose a variational principle for compressible and incompressible linear isotropic elasticity involving four dependent variables: the strain tensor, the augmented stress tensor, pressure and displacement. The variational formulation derived from the principle is analyzed employing a general result due to Brezzi. Finite element methods using the Galerkin and SBB methods are shown to converge for a wide family of finite element interpolations.