Rodolfo Araya, Manuel Solano, Patrick Vega:
A posteriori error analysis of an HDG method for the Oseen problem
We propose a residual-type a posteriori error estimator for a hybridizable discontinuous Galerkin method applied to the Oseen problem in 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 weighted 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.
This preprint gave rise to the following definitive publication(s):
Rodolfo ARAYA, Manuel SOLANO, Patrick VEGA: A posteriori error analysis of an HDG method for the Oseen problem. Applied Numerical Mathematics, vol. 146, pp. 291-308, (2019).