Coupling nonlinear Stokes and Darcy flow using mortar finite elements (Q643360)

The authors study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of a shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. The authors recast the coupled Stokes-Darcy system into a reduced matching problem on the interface using a mortar space approach. They prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. The authors further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of defective boundary conditions.