Hierarchical basis error estimators for Raviart-Thomas discretizations of arbitrary order

We consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations. In particular, we present a hierarchical basis error estimator for Raviart-Thomas mixed finite element discretizations of order l on simplicial triangulations. The introduction of the error estimator is based on the principle of defect correction In higher order of the flux ansatz space, we obtain an easily computable, efficient and reliable a posteriori error estimator for the flux error and for flux and primal error components.