Self-equilibrated residual based error estimation on 1-irregular meshes in finite elasticity

Abstract

We consider well-established techniques for the residual error estimation of finite element approximations applied to problems in finite elasticity. The element implicit residual method and the method of self-equilibration are applied to nearly incompressible and anisotropic finite strain elastic cases. Our contribution regarding the residual error estimation concerns generalising the approach to 1-irregular meshes. That is, we recover equilibrating element tractions in the presence of compatibility enforcing constraints. The generalisations are illustrated using numerical experiments. The considered variants of the estimators are compared.