On the asymptotic exactness of an error estimator for the lowest-order Raviart--Thomas mixed finite element

Abstract

In this paper we analyze an error estimator for the lowest-order triangular Raviart--Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385--395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.