On the asymptotic exactness of error estimators based on the equilibrated residual method for quadrilateral finite elements (Q1760124)

The paper analyzes the equilibrated residual method for a posteriori error estimation of finite element approximation on quadrilateral elements. The author proves that the estimator obtained by solving the element residual problems over an infinite dimensional space \(H^{1}(K)/ \mathbb{R}\) is asymptotically exact in the energy norm for the regular solutions provided that the degree of approximation is of odd order and the elements are rectangles.