Edge residuals dominate A posteriori error estimates for low order finite element methods

We prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on the error of linear finite element m ethods both in H-1- and L-2-norms. We present two proofs: one uses the stan dard L-2-projection and the other relies on a new, weighted Clement-type in terpolation operator.