Approximation of the Stokes problem by residual-free macro bubbles

Abstract

Linear-constant velocity-pressure elements are enriched with residualfree macro bubbles. Static condensation prompts a stabilized method for this element, where mesh-dependent jumps of the normal stress are added across internal edges of the underlying macroelements. This procedure renders the SIMPLEST element stable. 1 Introduction The Stokes problem models creeping flows, which are flows where inertia can be neglected with respect to diffusion and source terms in the momentum equilibrium equation. Applications of this model to some subsurface flows, using variable viscosity coefficients, has gained new impetus with the increased concern in environmental conservation issues. In addition to these applications, the Stokes operator is a major component of the Navier-Stokes equations, and therefore a building block to understanding the different flow regimes in a more complex fluid dynamics problem. Approximation of the Stokes problem using finite element methods produces a mixed variati...