Solution of porous medium type systems by linear approximation schemes. (English) Zbl 0744.65060

The aim of this paper is to analyze the convergence of linear semi- discrete and discrete schemes for non-linear degenerate parabolic systems. Convergence analysis for the problem is presented in various theorems. Numerical experiments are also presented for the validity of the proposed methods.


65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K65 Degenerate parabolic equations
76S05 Flows in porous media; filtration; seepage
Full Text: DOI EuDML


[1] Alt, H.W., Luckhaus, S. (1983): Quasilinear Elliptic-Parabolic Differential Equations. Math. Z.183, 311–341 · Zbl 0508.35046
[2] Aronson, D., Crandall, M.G., Peletier, L.A. (1982): Stabilisation of solutions of a degenerate nonlinear diffusion problem. Nonlinear analysis. TMA6, 1001–1022 · Zbl 0518.35050
[3] Berger, A.E., Brezis, H., Rogers, J.C.W. (1979): A numerical method for solving the problemu t f(u)=0. R.A.I.R.O. Anal. Numer.13, 297–312
[4] Di Benedetto, E., Hoff, D. (1984): An interface tracking alogrithm for the porous medium equation. Trans. Amer. Math. Soc.284, 463–500 · Zbl 0564.76090
[5] Gajewski, H., Gröger, K., Zacharias, K. (1974): Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin
[6] Gravelean, J.L., Jamet, P. (1971): A finte dimensional approach to some degenerate nonlinear parabolic equations. SIAM J. Appl. Math.20, 199–223 · Zbl 0226.65065
[7] Kačur, J: On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces I, II. Math. Z. (to appear)
[8] Ladyzenskaja, O.A. (1964): Linear and quasilinear elliptic equations. Nauka, Moskow
[9] Magenes, E., Nochetto, R.H., Verdi, C. (1987): Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. Math. Mod. Numer. Anal.21, 655–678 · Zbl 0635.65123
[10] MacCamy, R.C., Socolovsky, E. (1985): A numerical procedure for the porous media equation. Comp. Math. Appl.11, 315–319 · Zbl 0608.76083
[11] Nečas, J. (1967): Les methodes directes en theorie des equations elliptiques. Academia, Prague
[12] Passo, R.D., Luckhaus, S. (1987): A degenerate diffusion equation not in divergence form. J. Differ. Equations69, 1–14 · Zbl 0688.35045
[13] Tomoeda, K., Mimura, M. (1983): Numerical approximations to interface curves for a porous media equation. Hiroshima Math. J.13, 273–294 · Zbl 0537.76065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.