An Adaptive Refinement Strategy Based on Equilibrated Flux Error Estimation for Elliptic Problems in Conforming Finite Element Settings

Abstract In this work we demonstrate the effectiveness of an a-posteriori error estimator based on the Prager Synge theorem for a wide range of problems: smooth problem, problem with a steep gradient, problem with a boundary condition induced singularity, problem with varying conductivity. A very simple but innovative strategy is presented for deciding on h or p adaptivity. Exponential convergence rates were obtained for all test problems. The reconstruction of H(div) compatible functions is applied to meshes with hanging nodes. We believe this work represents an important step towards a cost effective hp -adaptive strategy with a posteriori error estimation.