Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems

Abstract

We present a patch-based equilibrated flux recovery procedure for the conforming finite element approximation to diffusion problems. The recovered flux is computed as the solution to a local constraint-free minimization problem on each patch. The approach is valid for higher order conforming elements in both two and three dimensions. The resulting estimator admits guaranteed reliability and the robust local efficiency is proved under the quasi-monotonicity condition of the diffusion coefficient. Numerical experiments are given to confirm the theoretical results.