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2003-28

On Korn's first inequality for quadr

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