## 04-12

#### Inf-sup stable non-conforming finite elements of arbitrary order on triangles

**Preprint series:** 04-12, 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 finite elements, inf-sup stability, Stokes problem

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