Abstract or Additional Information
The Brinkman problem can be viewed as a convex combination of the Stokes' equations and Darcy's equation. The former model the flow of a freely flowing fluid and the later the flow ofa fluid in a porous medium, and the convex combination of the two was introduced as a model for flows intermediate between these two extremes.
The analysis and numerical approximation of Stokes' equationsand the Darcy equation are well understood but quite distinct. In particular, numerical schemes designed for one system maynot be stable and/or convergent for the other. In this talk a mixed formulation of the Brinkman problem is introduced which is amenable to analysis for all choices of the parameters. Numerical schemes using this formulation will then be considered. This if joint work with Jason Howell at the College of Charleston, SC.