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.