HIERARCHICAL ERROR ESTIMATORS FOR LOWEST-ORDER MIXED FINITE ELEMENT METHODS

Abstract. In this work we study two a posteriori error estimators of hierarchical type for lowest-order mixed finite element methods. One estimator is computed by solving a global defect problem based on the splitting of the lowest-order Brezzi–Douglas–Marini space, and the other estimator is locally computable by applying the stan-dard localization to the first estimator. We establish the reliability and efficiency of both estimators by comparing them with the stan-dard residual estimator. In addition, it is shown that the error es-timator based on the global defect problem is asymptotically exact under suitable conditions. 1