The main focus of this paper is on the evaluation of local a posteriori error estimation techniques for the finite element method (FEM). The standard error estimation techniques are presented for the coupled displacement fields appearing in elasticity problems. The two error estimators, the element residual method (ERM) and Zienkiewicz–Zhu (ZZ) patch recovery technique, are evaluated numerically and then used as drivers for a mesh adaptation process. The results demonstrate the advantages of employing a posteriori error estimators for obtaining finite element solutions with a pre-specified error tolerance. Of the two methods, the ERM is shown to produce adapted meshes that are similar to those adapted by the exact error. Furthermore, the ERM provides higher quality estimates of the error in the global energy norm when compared to the ZZ estimator.
A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems
