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Anisotropic Wilson element with conforming finite element approximation for a coupled continuum pipe‐flow/Darcy model in Karst aquifers
Author(s) -
Liu Wei,
Zhao Qingli,
Li Xindong,
Li Jin
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3341
Subject(s) - mathematics , uniqueness , anisotropy , darcy–weisbach equation , finite element method , darcy's law , mathematical analysis , porous medium , flow (mathematics) , mechanics , geometry , porosity , physics , geology , geotechnical engineering , structural engineering , engineering , quantum mechanics
Numerical method for a coupled continuum pipe‐flow/Darcy model describing flow in porous media with an embedded conduit pipe is considered. Wilson element on anisotropic mesh is used to solve the Darcy equation on porous matrix. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in L 2 and H 1 norms are established independent of the regularity condition on the mesh. Numerical examples show the efficiency of the presented scheme. With the same number of nodal points, the results using Wilson element on anisotropic mesh are much better than those of the same element and Q 1 element on regular mesh. Copyright © 2014 John Wiley & Sons, Ltd.