Non-Matching Mortar Discretization Analysis for the Coupling Stokes-Darcy Equations
Marcus Sarkis | Galvis, Juan Carlos
inf-sup condition | error estimates | mortar finite elements | multiphisics | porous media flow | incompressible fluid flow | Lagrange multipliers | saddle point problems | nonmatching grids | discontinuous coefficients
We consider the coupling across an interface of fluid and porous media flows with Beavers-Joseph-Saffman transmission conditions. Under adequate choices of Lagrange multipliers on the interface we analyze inf-sup conditions and optimal a priori error estimates associated to the continuous and to the discrete formulations of the Stokes-Darcy system. We allow the meshes of the two regions to be nonmatching 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.