Volume 26, pp. 350-384, 2007.

Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations

Juan Galvis and Marcus Sarkis

Abstract

We consider the coupling across an interface of fluid and porous media 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 the 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 on the a priori error bounds do not depend on the viscosity, permeability and ratio of mesh parameters. Numerical experiments are presented.

Full Text (PDF) [595 KB]

Key words

inf-sup condition, error estimates, mortar finite elements, multiphysics, porous media flow, incompressible fluid flow, Lagrange multipliers, saddle point problems, non-matching grids, discontinuous coefficients

AMS subject classifications

65N30, 65N15, 65N12, 35Q30, 35Q35, 76D033, 76D07

< Back