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A study of free boundary problems of fluid flow in porous media by mixed methods. (English) Zbl 0929.35179

Athanasopoulos, I. (ed.) et al., Free boundary problems: theory and applications. Proceedings of the conference, Crete, Greece, June 8–14, 1997. Boca Raton, FL: Chapman & Hall/CRC. Chapman Hall/CRC Res. Notes Math. 409, 3-13 (1999).
Summary: The flow of fluids in porous media is studied as a free or moving boundary problem by the mixed method. In particular, a new weak formulation for the problem of seepage of fluids through a porous media is discussed and analyzed mathematically and numerically. The new formulation is in a mixed form and is suitable for the use of mixed finite element methods in the numerical approximation. It is proved that the weak formulation and its finite element discretization have a solution which can be approximated by a sequence of regularized problems.
For the entire collection see [Zbl 0919.00052].

MSC:

35R35 Free boundary problems for PDEs
76S05 Flows in porous media; filtration; seepage
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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