Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods

Abstract

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 methods both in H1 - and L2 -norms. We present two proofs: one uses the standard L2 -projection and the other relies on a new, weighted Clément-type interpolation operator.