STABILIZED FINITE ELEMENT METHODS FOR THE BRINKMAN EQUATION ON FITTED AND FICITITIOUS DOMAINS

Abstract

The parameter dependent Brinkman equation can be used to model viscous and porous flow. The equation covers a family of problems, ranging from the Stokes problem to the Darcy problem. We apply the stabilization methods; the pressure stabilized petrov--galerkin (PSPG) method and the continuous interior penalty (CIP) method, on the Brinkman equation with weakly imposed boundary conditions by the Nitsche method. An a priori error estimate is proved for the CIP stabilization with the Nitsche method. We look at operator preconditioning for these stabilized problems with appropriate norms. We also explore a fictitious domain method and stabilize the cut elements with ghost-penalties.