### 2004-12

by Matthies, G., Tobiska, L..

**Series:** 2004-12, Preprints

- MSC:
- 65N12 Stability and convergence of numerical methods
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

**Abstract:**

We introduce a family of scalar non-conforming finite elements of arbitrary

order $k\ge 1$ with respect to the $H^1$-norm on triangles. Their

vector-valued versions generates together

with a discontinuous pressure approximation of order $k-1$ an inf-sup stable

finite element pair of order $k$ for the Stokes problem in the energy norm.

For $k=1$ the well-known Crouzeix-Raviart element is recovered.

**Keywords:**

non-conforming fini