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

• ID: 2611, RIV: 10132879
• ISSN: 0749-159X, ISBN: neuvedeno
• zdroj: Numerical Methods for Partial Differential Equations
• klíčová slova: finite element method; local projection; Oseen problem; stability; error estimates
• autoři: Petr Knobloch, Lutz Tobiska
• autoři z KNM: Knobloch Petr
• odkazy: http://efef2015.karlin.mff.cuni.cz/

Abstrakt

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.