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

Authors

  • Petr Knobloch,

    Corresponding author
    1. Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University in Prague, 186 75 Praha 8, Czech Republic
    • Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75 Praha 8, Czech Republic
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  • Lutz Tobiska

    1. Institute of Analysis and Computational Mathematics, Faculty of Mathematics, Otto von Guericke University Magdeburg, Magdeburg 39016 Germany
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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. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013

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