A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods

We consider some (anisotropic and piecewise constant) diffusion problems in domains of R, approximated by a discontinuous Galerkin method with polynomials of any degree. We propose an a posteriori error estimator based on gradient recovery by averaging. It is shown that this estimator gives rise to an upper bound where the constant is one up to some additional terms that guarantee reliability. The lower bound is also established. Moreover these additional terms are negligible when the recovered gradient is superconvergent. The reliability and efficiency of the proposed estimator is confirmed by some numerical tests.