TITLE:
A New Unified Stabilized Mixed Finite Element Method of the Stokes-Darcy Coupled Problem: Isotropic Discretization
AUTHORS:
Houédanou Koffi Wilfrid
KEYWORDS:
Coupled Stokes and Darcy Flows, Nonconforming Finite Element Method, Crouzeix-Raviart Element
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.7,
July
29,
2021
ABSTRACT: In this paper, we develop an a-priori error analysis of a new unified mixed finite element method for the coupling of fluid flow with porous media flow in RN, N ∈ {2,3}, on isotropic meshes. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The approach utilizes a modification of the Darcy problem which allows us to apply a variant nonconforming Crouzeix-Raviart finite element to the whole coupled Stokes-Darcy problem. The well-posedness of the finite element scheme and its convergence analysis are derived. Finally, the numerical experiments are presented, which confirm the excellent stability and accuracy of our method.