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Girault, V. and Raviart, P.-A. (1986) Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. Springer Series in Computational Mathematics, Volume 5, Springer, Berlin.
https://doi.org/10.1007/978-3-642-61623-5

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.