Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations. (English) Zbl 1170.76024

Galvis, Juan; Sarkis, Marcus

ETNA, Electron. Trans. Numer. Anal. 26, 350-384 (2007).

Summary: We consider the coupling across an interface of fluid and porous medium flows with Beavers-Joseph-Saffman transmission conditions. Under an adequate choice of Lagrange multipliers on the interface, we analyze inf-sup conditions and optimal a priori error estimates associated with continuous and discrete formulations of this Stokes-Darcy system. We allow the meshes of the two regions to be non-matching across the interface. Using mortar finite element analysis and appropriate scaled norms, we show that the constants that appear in a priori error bounds do not depend on viscosity, permeability and ratio of mesh parameters. Numerical experiments are presented.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76S05	Flows in porous media; filtration; seepage
76D07	Stokes and related (Oseen, etc.) flows

Keywords:

inf-sup condition; finite elements; Lagrange multipliers; Beavers-Joseph-Saffman transmission conditions