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Keywords:
nonconforming finite element method; inf-sup condition; incompressible flow problem
Summary:
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 $n$th order accuracy in the energy norm called $P_n^{}$ elements. For $n\le 3$ we show that the stability condition holds if the velocity space is constructed using the $P_n^{}$ elements and the pressure space consists of continuous piecewise polynomial functions of degree $n$.
References:
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