[02351] THE WELL-POSEDNESS AND DISCONTINUOUS GALERKIN APPROXIMATION FOR THE NON-NEWTONIAN STOKES–DARCY–FORCHHEIMER COUPLING SYSTEM

Session Time & Room : 5B (Aug.25, 10:40-12:20) @D101

Type : Contributed Talk

Abstract : We establish the well-posedness theorem and study discontinuous Galerkin $($DG$)$ approximation for the non-Newtonian Stokes--Darcy--Forchheimer system modeling the free fluid coupled with the porous medium flow with shear/velocity-dependent viscosities. The unique existence is proved by using the theory of nonlinear monotone operator. In particular, we prove a coupled inf-sup condition to show the existence of pressure in $L^2(\Omega_1) \times L^\frac{3}{2}(\Omega_2)$. We also explore the convergence of the Picard iteration for the continuous problem. Moreover, we apply the DG method with $\mathbb{P}_k/\mathbb{P}_{k-1}$ element for numerical discretization and obtain the well-posedness, stability, and error estimate. For the discrete problem, we also investigate the convergence of the Picard iteration. The theoretical results are confirmed by the numerical examples.