# Stokes-Darcy Coupling

## Manuela Redl BSc

April 1, 2014, 3:30 p.m. S2 059

This talk is about the coupling of Stokes and Darcy equations. The model problem we consider consists of a fluid region $\Omega_1$ and a porous medium region $\Omega_2$. In $\Omega_1$ we assume a Stokes flow and in $\Omega_2$ we suppose that Darcy's law is satisfied. The two regions are separated by an interface. The Stokes and the Darcy equations must be coupled by suitable interface conditions.
In the first part of the talk, we will derive a weak formulation for the problem.
Then we will show existence and uniqueness of a solution to the weak problem using Brezzi's theorem.
In the end, further weak formulations of the problem will be discussed.