Geodesic
On stability of the $P^{\rm mod}_ n/P_ n$ element for incompressible flow problems
Applications of Mathematics, Tome 51 (2006) no. 5, pp. 473-493.

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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 $n$.
DOI : 10.1007/s10492-006-0017-7
Classification : 65N12, 65N30, 76D05, 76M10
Keywords: nonconforming finite element method; inf-sup condition; incompressible flow problem 
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Knobloch, Petr. On stability of the $P^{\rm mod}_ n/P_ n$ element for incompressible flow problems. Applications of Mathematics, Tome 51 (2006) no. 5, pp. 473-493. doi : 10.1007/s10492-006-0017-7. http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0017-7/

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