Volume 2, Issue 4
On Korn's First Inequality for Quadrilateral Nonconforming Finite Elements of First Order Approximation Properties

P. Knobloch & L. Tobiska

DOI:

Int. J. Numer. Anal. Mod., 2 (2005), pp. 439-458

Published online: 2005-02

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  • Abstract

We investigate the Korn first in equality for quadri lateral nonconforming finite elements of first order approximation properties and clarify the dependence of the constant in this in equality 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

  • AMS Subject Headings

65N12 65N30 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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