Nonstandard nonconforming approximation of the Stokes problem, I: Periodic boundary conditions
Jean Luc Guermond 11 Department of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843-3368, USA
Received by the editors October 25, 2004 and, in revised form, November 5, 2004
This paper analyzes a nonstandard form of the Stokes problem where the mass conservation equation is expressed in the form of a Poisson equation for the pressure. This problem is shown to be wellposed in the dimensional torus. A nonconforming approximation is proposed and, contrary to what happens when using the standard saddle-point formulation, the proposed setting is shown to yield optimal convergence for every pairs of approximation spaces.
AMS subject classifications: 65N30, 35Q30, 76D07
Key words: Stokes equations; finite elements; nonconforming approximation; incompressible flows and Poisson equation