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Finite element analysis of thermally coupled nonlinear Darcy flows
Author(s) -
Zhu Jiang
Publication year - 2010
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.20412
Subject(s) - uniqueness , finite element method , mathematics , nonlinear system , convergence (economics) , partial differential equation , mixed finite element method , mathematical analysis , weak solution , darcy's law , extended finite element method , viscosity , partial derivative , porous medium , physics , porosity , thermodynamics , materials science , quantum mechanics , economics , economic growth , composite material
We consider a coupled system describing nonlinear Darcy flows with temperature dependent viscosity and with viscous heating. We first establish existence, uniqueness, and regularity of the weak solution of the system of equations. Next, we decouple the coupled system by a fixed point algorithm and propose its finite element approximation. Finally, we present convergence analysis with an error estimate between continuous solution and its iterative finite element approximation.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010