A robust a posteriori error estimator for divergence-conforming discontinuous Galerkin methods for the Oseen equation - Khan, Arbaz; Kanschat, Guido (SIAM journal on numerical analysis, 2020)
In this paper, a robust a posteriori error estimator for divergence-conforming discontinuous Galerkin methods for the Oseen equation is presented. Upper and local lower bounds for the velocity-pressure error in terms of the energy norm and a seminorm associated with the convective term are derived. We prove that the ratio of upper and lower bounds is independent of the Reynolds number. Thus the proposed estimator is fully robust. Specific numerical experiments are discussed to validate the theoretical results.