Weak Galerkin Method for Coupling Stokes and Darcy-Forchheimer Flows (Journal of Computational Mathematics, 2025)
In this paper, we introduce the weak Galerkin (WG) method for solving the coupledStokes and Darcy-Forchheimer flows problem with the Beavers-Joseph-Saffman interfacecondition in bounded domains. We define the WG spaces in the polygonal meshes andconstruct corresponding discrete schemes. We prove the existence and uniqueness of theWG scheme by the discrete inf-sup condition and monotone operator theory. Then, wederive the optimal error estimates for the velocity and pressure. Numerical experimentsare presented to verify the efficiency of the WG method.