Title:         Quadratic velocity/linear pressure Stokes elements

Authors:       Douglas N. Arnold and Jinshui Qin

Source:        in: "Advances in Computer Methods for Partial Differential
Equations-VII" (R. Vichnevetsky, D. Knight, G. Richter, eds.), IMACS, 1992,
pp. 28-34

Status:        Published

Abstract:  We study the finite element approximation of the stationary
Stokes equations in the velocity-pressure formulation using continuous
piecewise quadratic functions for velocity and discontinuous piecewise
linear functions for pressure.  For some meshes this method is unstable,
even after spurious pressure modes are removed.  For other meshes there
are spurious local pressure modes, but once they are removed the method
is stable, and in particular, the velocity converges with optimal order.
On yet other meshes there are no spurious pressure modes and the method
is stable and optimally convergent for both pressure and velocity.

Keywords:      finite element, Stokes equations

URL:           http://ima.umn.edu/~arnold/papers/imacs92.pdf