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Numerical solution of steady-state porous flow free boundary problems. (English) Zbl 0447.76074

MSC:
76S05 Flows in porous media; filtration; seepage
35Q99 Partial differential equations of mathematical physics and other areas of application
35R35 Free boundary problems for PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49J40 Variational inequalities
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References:
[1] Alt, H.W.: Strömungen durch inhomogene poröse Medien mit freiem Rand. J. Reine Angew. Math.305, 89-115 (1979) · Zbl 0392.76091 · doi:10.1515/crll.1979.305.89
[2] Alt, H.W.: A new numerical method for solving the dam problem. Proceeding Seminar on Free Boundary Problems. Sept.?Oct. 1979 (in press, 1980)
[3] Brezzi, F., Sacchi, G.: A finite element approximation of a variational inequality related to hydraulics. Laboratorio Anal. Numer. Consiglio Naz. Ricerche Pubbl.97 (1976) · Zbl 0353.76068
[4] Caffarelli, L.A., Riviere, N.M.: Existence and uniqueness for the problem of filtration through a porous medium. Notices Amer. Math. Soc.24, A576 (1977) · Zbl 0364.35041
[5] Comincioli, V.: A comparison of algorithm for some free boundary problems. Laboratorio Anal. Numer. Consiglio Naz. Ricerche Pubbl.79 (1976) · Zbl 0327.76043
[6] Comincioli, V., Guerri, L.: Numerical solution of free boundary problems in seepage flow with capillary fringe. Laboratorio Anal. Numer. Consiglio Naz. Ricerche Pubbl.96 (1976) · Zbl 0327.76043
[7] Comincioli, V., Guerri, L., Volpi, G.: Analisi numerica di un problema die frontiera libera connessa col moto di un fluido attraverso un mezzo poroso. Laboratorio Anal. Numer. Consiglio Naz. Ricerche Pubbl.17 (1971) · Zbl 0263.65075
[8] Cryer, C.W.: A survey of steady-state porous flow free boundary problems. M.R.C. Univ. Wisconsin,1657 (1976)
[9] Cryer, C.W.: A survey of trial free boundary methods for the numerical solution of free boundary problems. M.R.C. Univ. Wisconsin,1693 (1976)
[10] Cryer, C.W., Fetter, H.: The numerical solution of axis-symmetric free boundary porous flow well problems using variational inequalities. M.R.C. Univ. Wisconsin,1761 (1977) · Zbl 0416.76045
[11] Kikuchi, N.: An analysis of the variational inequalities of seepage flow by finite-element methods. Quart. Appl. Math.35, 149-163 (1977) · Zbl 0358.76061
[12] Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin Heidelberg New York: Springer 1966 · Zbl 0142.38701
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