A posteriori error analysis of an HDG method for the Oseen problem

Abstract

We propose a residual-type a posteriori error estimator for a hybridizable discontinuous Galerkin method applied to the Oseen problem in a gradient-velocity-pressure formulation. We state reliability and local efficiency results for our estimator with respect to an error measured in the natural norms, with constants depending explicitly on the physical parameters. A weighting function technique to control the L2-error of the velocity, and the approximation properties of the Oswald interpolation operator are the main ingredients in the analysis. Numerical experiments in three dimensions validate our theoretical results.