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Mixed finite elements applied to a nonlinear diffusion-convection equation modelling a problem of diphasic flow in porous media. (English) Zbl 0549.76063
Numerical methods in laminar and turbulent flow, Proc. 3rd Int. Conf., Seattle/Wash. 1983, 1047-1060 (1983).
[For the entire collection see Zbl 0544.00036.]
We study the numerical resolution of a nonlinear convection diffusion equation rewritten by G. Chavent [Lect. Notes Math. 503, 258-270 (1976; Zbl 0346.76071)]. We discretize the nonmonotonous term of convection by adaptation of the Godunov scheme which was studied by A. Y. Leroux [Math. Comput. 31, 848-872 (1977; Zbl 0378.65053)] in the case of finite differences to these finite elements.
MSC:
76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage
76R05 Forced convection
76M99 Basic methods in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs