ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. 70, 1 (2001)
pp. 75-84
A NUMERICAL APPROXIMATION OF NONFICKIAN FLOWS
WITH MIXING LENGTH GROWTH
IN POROUS MEDIA
R. E. EWING, Y. LIN and J. WANG
Abstract.
The nonFickian flow of fluid in porous media is complicated by the history effect which characterizes various mixing length growth of the flow, which can be modeled by an integro-differential equation. This paper proposes two mixed finite element methods which are employed to discretize the parabolic integro-differential equation model. An optimal order error estimate is established for one of the discretization schemes.
AMS subject classification.
Primary 76S05, 45K05, 65M12, 65M60, 65R20
Keywords.
Mixed finite element methods, up-scaling. multi-phase flow, non-
Fickian flow
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