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A weak Galerkin finite element method for a coupled Stokes‐Darcy problem
Author(s) -
Li Rui,
Li Jian,
Liu Xin,
Chen Zhangxin
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22146
Subject(s) - mathematics , piecewise , galerkin method , finite element method , darcy's law , conservation of mass , discontinuous galerkin method , mathematical analysis , partial differential equation , darcy–weisbach equation , stokes flow , conservation law , convergence (economics) , coupling (piping) , flow (mathematics) , porous medium , geometry , porosity , mechanics , physics , mechanical engineering , geotechnical engineering , engineering , economics , thermodynamics , economic growth
In this article, we introduce and analyze a weak Galerkin finite element method for numerically solving the coupling of fluid flow with porous media flow. Flows are governed by the Stokes equations in primal velocity‐pressure formulation and Darcy equation in the second order primary formulation, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers‐Joseph‐Saffman law. By using the weak Galerkin approach, we consider the two‐dimensional problem with the piecewise constant elements for approximations of the velocity, pressure, and hydraulic head. Stability and optimal error estimates are obtained. Finally, we provide several numerical results illustrating the good performance of the proposed scheme and confirming the optimal order of convergence provided by the weak Galerkin approximation. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1352–1373, 2017