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Analysis and finite element approximation of a coupled, continuum pipe‐flow/Darcy model for flow in porous media with embedded conduits
Author(s) -
Cao Yanzhao,
Gunzburger Max,
Hua Fei,
Wang Xiaoming
Publication year - 2011
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.20579
Subject(s) - porous medium , darcy's law , finite element method , mathematics , partial differential equation , convergence (economics) , electrical conduit , flow (mathematics) , mechanics , matrix (chemical analysis) , partial derivative , porosity , mathematical analysis , geology , geotechnical engineering , geometry , physics , engineering , materials science , structural engineering , mechanical engineering , economic growth , economics , composite material
Abstract We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. The mathematical well‐posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two‐dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1242–1252, 2011