Analysis of finite element methods for the Brinkman problem

Abstract: The parameter dependent Brinkman problem, covering a field of problems from the Darcy equations to the Stokes problem, is studied. A mathematical framework is introduced for analyzing the problem. Using this we prove uniform a priori and a posteriori estimates for two families of finite element methods. We also discuss Nitshe’s method for imposing boundary conditions. AMS subject classifications: 65N3