Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem (Communications in Computational Physics, 2020)
We consider a model of coupled free and porous media flow governed byStokes equation and Darcy's law with the Beavers-Joseph-Saffman interface condition.In this paper, we propose a new numerical approach for the Stokes-Darcy system. Theapproach employs the classical finite element method for the Darcy region and theweak Galerkin finite element method for the Stokes region. We construct corresponding discrete scheme and prove its well-posedness. The estimates for the corresponding numerical approximation are derived. Finally, we present some numerical experiments to validate the efficiency of the approach for solving this problem.
Keywords: Finite element methods; weak Galerkin finite element methods; weak gradient; Stokes equations; Darcy's equation.