A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements

For the lowest order Raviart-Thomas mixed finite element, we derive an a posteriori error estimator that provides actual, guaranteed computable upper bounds on the error in the flux variable regardless of jumps in the material coefficients across interfaces. Moreover, the estimator is efficient in that it provides a local lower bound on the error up to a constant that is independent of the solution and the local mesh-size. The estimator may be evaluated at virtually no additional cost compared to the evaluation of the finite element approximation itself.