A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model (Advances in Applied Mathematics and Mechanics, 2018)
In this work, we study numerical methods for a coupled fluid-porous mediaflow model. The model consists of Stokes equations and Darcy's equations in twoneighboring subdomains, coupling together through certain interface conditions. Theweak form for the coupled model is of saddle point type. A mortar finite elementmethod is proposed to approximate the weak form of the coupled problem. In ourmethod, nonconforming Crouzeix-Raviart elements are applied in the fluid subdomainand the lowest order Raviart-Thomas elements are applied in the porous mediasubdomain; meshes in different subdomains are allowed to be nonmatching on thecommon interface; interface conditions are weakly imposed via adding constraint inthe definition of the finite element space. The well-posedness of the discrete problemand the optimal error estimate for the proposed method are established. Numericalexperiments are also given to confirm the theoretical results.