SCAIM Seminar: Ricardo Oyarzua, UBC

Abstract:

In this talk we a introduce mixed finite element method for the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. We consider mixed formulations in both the Stokes domain and the Darcy region, which yields the introduction of the traces of the porous media pressure and the fluid velocity as suitable Lagrange multipliers. Then, considering generic finite element spaces with some technical conditions, we apply the Babuska-Brezzi theory together with a classical result on projection methods for Fredholm operators of index zero to show stability, convergence, and a priori error estimates for the associated Galerkin scheme. Finally, we generalize the previous results and introduce a mixed finite element method for the coupling of fluid flow with nonlinear porous media flow. This is joint work with G.N. Gatica (University of Concepcion) and F.-J. Sayas (University of Delaware).