Local projection stabilization for the Stokes equation with Neumann condition

Abstract

The local projection stabilization (LPS) method is already an established method for stabilizing saddle-point problems and convection–diffusion problems. The a priori error analysis is usually done for homogeneous Dirichlet data. It turns out that without Dirichlet conditions the situation is more involved, because additional boundary terms appear in the analysis. The standard approach can be modified by using additional stabilization terms on the non-Dirichlet boundary parts. We show that such terms lead to a similar a priori estimate as the classical LPS method but in a stronger norm.