Preprint A667/2010
FETI-DP for Stokes-Mortar-Darcy Systems
Marcus Sarkis | Galvis , Juan
Keywords: Stokes and Darcy coupling | FETI-DP | mortar elements | preconditioners
We consider the coupling across an interface of a fluid flow and a porous media flow. The differential equations involve Stokes equations in the fluid region, Darcy equations in the porous region, plus a coupling through an interface with Beaver-Joseph-Saffman transmission conditions, see \cite{MR2318811,layton,galvissarkis2005,MR2344200}. The discretization consists of $P2$-$P0$ finite elements in the fluid region, the lowest order triangular Raviart-Thomas finite elements in the porous region, and the mortar piecewise constant Lagrange multipliers on the interface. Due to the small values of the permeability parameter $\kappa$ of the porous medium, the resulting discrete symmetric saddle point system is very ill conditioned. Preconditioning is needed in order to efficiently solve the resulting discrete system. The purpose of this work is to present some preliminary results on the extension of the modular FETI type preconditioner proposed in \cite{galvissarkisDD16,gsSUMITTED} to the multidomain FETI-DP case.