H(div)-conforming finite elements for the brinkman problem
Research output: Contribution to journal › Article › Scientific › peer-review
The Brinkman equations describe 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 the symmetric interior penalty Galerkin method to obtain a stable formulation. We show that the formulation is 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.
|Number of pages||22|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - Nov 2011|
|MoE publication type||A1 Journal article-refereed|
- a posteriori error estimates, Brinkman problem, DarcyStokes equation, H(div)-conforming, Nitsche's method, postprocessing, SIPG