%0 Journal Article
%T A New Unified Stabilized Mixed Finite Element Method of the Stokes-Darcy Coupled Problem: Isotropic Discretization
%A Hou¨¦danou Koffi Wilfrid
%J Journal of Applied Mathematics and Physics
%P 1673-1706
%@ 2327-4379
%D 2021
%I Scientific Research Publishing
%R 10.4236/jamp.2021.97112
%X 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 R<sup><em>N</em></sup>, <em>N</em> ¡Ê {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.
%K Coupled Stokes and Darcy Flows
%K Nonconforming Finite Element Method
%K Crouzeix-Raviart Element
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=110938