Guaranteed and asymptotically exact a posteriori error estimator for lowest-order Raviart-Thomas mixed finite element method

In this paper we propose and analyze some a posteriori error estimator for the lowest-order triangular Raviart-Thomas mixed finite element method. This error estimator is a simple modification of the ones proposed in Vohralik (2007) [34] and Ainsworth (2008) [1], and relies on the use of a superconvergent vector approximation. It is shown that the new error estimator not only guarantees an upper bound on the vector error for general triangulations but also achieves asymptotic exactness for mildly structured triangulations. To establish asymptotic exactness on subdomains, we also derive some interior superconvergence results for the lowest-order Raviart-Thomas mixed finite element. (c) 2021 IMACS. Published by Elsevier B.V. All rights reserved.