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On stability of the P modn /P n element for incompressible flow problems

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Abstract

It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of nth order accuracy in the energy norm called P modn elements. For n ≤ 3 we show that the stability condition holds if the velocity space is constructed using the P modn elements and the pressure space consists of continuous piecewise polynomial functions of degree n.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Numerical Mathematics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Petr Knobloch

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  1. Petr Knobloch
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This research has been supported by the Grant Agency of the Czech Republic under the grant No. 201/05/0005 and by the grant MSM 0021620839.

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Knobloch, P. On stability of the P modn /P n element for incompressible flow problems. Appl Math 51, 473–493 (2006). https://doi.org/10.1007/s10492-006-0017-7

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  • DOI: https://doi.org/10.1007/s10492-006-0017-7

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