A hybrid a posteriori error estimator for conforming finite element approximations

This paper introduces a hybrid a posteriori error estimator for the conforming finite element method, which may be regarded as a combination of the explicit residual and the improved ZZ error estimators. With comparable cost, the hybrid estimator is more accurate than the residual estimator. It is shown that the hybrid estimator is reliable on all meshes, unlike estimators of the ZZ type. Moreover, the reliability constant is independent of the jump of the diffusion coefficients for elliptic interface problems under the monotonicity assumption of the coefficients. Finally, numerical examples confirm the robustness of the estimator with respect to coefficient jumps and also better effectivity index compared to the residual estimator.