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A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model

Part of: Incompressible viscous fluids Partial differential equations, boundary value problems Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  17 January 2017

Peiqi Huang ,
Jinru Chen  and
Mingchao Cai
Peiqi Huang*
Affiliation:
Department of Applied Mathematics, Nanjing Forestry University, Nanjing, Jiangsu 210037, China Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, China
Jinru Chen*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, China
Mingchao Cai*
Affiliation:
Department of Mathematics, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21251, USA
*
*Corresponding author. Email:pqhuang@njfu.edu.cn (P. Q. Huang), jrchen@njnu.edu.cn (J. R. Chen), cmchao2005@gmail.com (M. C. Cai)
*Corresponding author. Email:pqhuang@njfu.edu.cn (P. Q. Huang), jrchen@njnu.edu.cn (J. R. Chen), cmchao2005@gmail.com (M. C. Cai)
*Corresponding author. Email:pqhuang@njfu.edu.cn (P. Q. Huang), jrchen@njnu.edu.cn (J. R. Chen), cmchao2005@gmail.com (M. C. Cai)
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Abstract

In this work, we study numerical methods for a coupled fluid-porous media flow model. The model consists of Stokes equations and Darcy's equations in two neighboring subdomains, coupling together through certain interface conditions. The weak form for the coupled model is of saddle point type. A mortar finite element method is proposed to approximate the weak form of the coupled problem. In our method, nonconforming Crouzeix-Raviart elements are applied in the fluid subdomain and the lowest order Raviart-Thomas elements are applied in the porous media subdomain; Meshes in different subdomains are allowed to be nonmatching on the common interface; Interface conditions are weakly imposed via adding constraint in the definition of the finite element space. The well-posedness of the discrete problem and the optimal error estimate for the proposed method are established. Numerical experiments are also given to confirm the theoretical results.

Keywords

Mortar methodnonconforming elementmixed elementinf-sup conditionStokes equationsDarcy's equationserror estimate

MSC classification

Secondary: 65N12: Stability and convergence of numerical methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N55: Multigrid methods; domain decomposition 76D07: Stokes and related (Oseen, etc.) flows 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017 , pp. 596 - 620
Copyright
Copyright © Global-Science Press 2017 

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