Mat-1.3656 Seminar on numerical analysis and computational science

Monday Feb 22 , 2010, room U322 at 14.15, Eirola & Stenberg

Juho Könnö, A!

H(div)-conforming finite elements and Nitsche's method for the Brinkman problem

The Brinkman equation describes the flow of a viscous fluid in a porous matrix. Mathematically the Brinkman model is a parameter-dependent combination of both the Darcy and Stokes models. We introduce a dual mixed framework for the problem, and use H(div)-conforming finite elements with Nitsches method to obtain a stable formulation. We show the formulation to be stable in a mesh-dependent norm for all values of the parameter. We also introduce a postprocessing scheme for the pressure along with a residual-based a posteriori estimator, which is shown to be efficient and reliable for all parameter values. Furthermore, hybridization of the system is considered.