Title:         On nonconforming linear-constant elements for some
variants of the Stokes equations

Authors:       Douglas N. Arnold

Source:        Istit. Lombardo Accad. Sci. Lett. Rend. A 127 (1993), pp. 83-93

Status:        Published

Abstract:  Nonconforming piecewise linear finite elements for the
velocity field and piecewise constant elements for the pressure field
give a simple stable, optimal order approximation to the Stokes
equations, but are not stable for the equations of incompressible
elasticty, which differ from the Stokes equations only in that the
vector Laplace operator is replaced by the Lame operator.  However,
we show that if we replace the divergence by the rotation, then the
nonconforming linear-constant element is stable both for the system
involving the Laplacian and for that involving the Lame operator.
Finally we discuss an application to the Reissner-Mindlin plate.

Keywords:      Stokes equations, mixed finite element
method,nonconforming finite elements, Reissner-Mindlin plate

Subj. class.:  65N30,65N12,76M10,76D07,73K10

URL:           http://ima.umn.edu/~arnold/papers/ncstokes.pdf