A Posteriori Error Estimators Based on Equilibrated Fluxes

Abstract

We consider the conforming of finite element approximations of reactiondiffusion problems. We propose new a posteriori error estimators based on H(div)- conforming finite elements and equilibrated fluxes. It is shown that these estimators give rise to an upper bound where the constant is one in front of the indicator, up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh and the local variation of the coefficients. We further analyze the convergence of an adaptive algorithm. The reliability and efficiency of the proposed estimators are confirmed by various numerical tests. © 2010, Institute of Mathematics, NAS of Belarus. All rights reserved.