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Chen, W. and Wang, Y. (2014) A Posteriori Error Estimate for H(div) Conforming Mixed Finite Element for the Coupled Darcy-Stokes System. Journal of Computational and Applied Mathematics, 255, 502-516.
https://doi.org/10.1016/j.cam.2013.05.021

has been cited by the following article:

• 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.