### 2003-28

by Knobloch, P., Tobiska, L..

**Series:** 2003-28, Preprints

- MSC:
- 65N12 Stability and convergence of numerical methods
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
- 65N15 Error bounds

**Abstract:**

We investigate the Korn first inequality for quadrilateral nonconforming finite

elements of first order approximation properties and clarify the dependence

of the constant in this inequality on the discretization parameter $h$. Then

we use the nonconforming elements for approximating the velocity in a

discretization of the Stokes equations with boundary conditions involving

surface forces and, using the result on the Korn inequality, we prove error

estimates which are optimal for the pressure and suboptimal for the velocity.

**Keywords:**

Nonconforming finite elements, Korn's inequality, Stokes equations, error estimates