Robust recovery-type a posteriori error estimators for streamline upwind/Petrov Galerkin discretizations for singularly perturbed problems

摘要

In this paper, we investigate adaptive streamline upwind/Petrov Galerkin (SUPG) methods for second order convection-diffusion-reaction equations with singular perturbation in a new dual norm presented in [17]. The flux can be recovered in two different manners: local averaging in conforming H(div) spaces, and weighted global L~2 projection onto conforming H(div) spaces. We further propose a recovery stabilization procedure, and provide completely robust a posteriori error estimators with respect to the singular perturbation parameter ε. Numerical experiments are provided to confirm theoretical results and to show that the estimated errors depend on the degrees of freedom uniformly in the diffusion parameter ε.