Stabilized FEM with Anisotropic Mesh Refinement for the Oseen Problem

Abstract

Nonstationary incompressible flow problems can be split into auxiliary problems of Oseen type. We present the analysis of conforming stabilized Galerkin methods of SUPG/PSPG-type with equal-order interpolation of velocity/pressure and with emphasis on anisotropic mesh refinement in boundary layers. We prove a modified inf-sup condition with a constant independent of the viscosity and of critical parameters of the mesh. Numerical tests confirm the results.