Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem

• ID: 2619, RIV: 10104796
• ISSN: 0749-159X, ISBN: not specified
• source: Numerical Methods for Partial Differential Equations
• keywords: finite element method; local projection; Oseen problem; stability; error estimates
• authors: Petr Knobloch, Lutz Tobiska
• authors from KNM: Knobloch Petr

Abstract

We consider a class of local projection stabilizations with projection spaces defined on (possibly) overlapping sets applied to the Oseen problem. We prove that the underlying bilinear form satisfies an inf-sup condition with respect to a stronger norm than coercivity suggests. A modification of the stabilization of the convection allows an optimal estimation of the consistency error. A priori estimates in the stronger norm and in the L2 norm for the pressure are established. Discontinuous pressure approximations are included in the analysis.