Robust residual-based a posteriori Arnold-Winther mixed finite element analysis in elasticity

This paper presents a residual-based a posteriori error estimator for the Arnold-Winther mixed finite element that utilises a post-processing for the skew-symmetric part of the strain. Numerical experiments verify the proven reliability and efficiency for suitable approximation of the skew-symmetric deformation gradient. Numerical evidence supports that the L2-stress error estimator is robust in the Poisson ratio and allows stable error control even in the incompressible limit.