Averaging technique for FE – a posteriori error control in elasticity. Part II: λ-independent estimates

Abstract

In the second part of our investigation on a posteriori error estimates and a posteriori error control in finite element analysis in elasticity, we focus on robust a posteriori error bounds. First we establish a residual-based a posteriori error estimate which is reliable and efficient up to higher-order terms and λ-independent multiplicative constants; the Lamé constant λ steers the incompressibility. Second we show the robust efficiency and reliability of averaging techniques in certain norms. Numerical evidence supports that the reliability of depends on the smoothness of given right-hand sides and is independent of the structure of a shape-regular mesh.