An interface tracking algorithm for the porous medium equation. (English) Zbl 0564.76090

DiBenedetto, E.; Hoff, David

Trans. Am. Math. Soc. 284, 463-500 (1984).

The convergence of a finite difference scheme for the Cauchy problem for equation \(u_ t=(u^ m)_{xx}\), \(m>1\), is studied. Not only approximate solutions, but also approximate interfaces are generated as well as the scheme is shown to contain a vanishing viscosity term. Various lemmas and theorems are proved. Numerical results are at last reported for applications in porous media theory.

Reviewer: V.Boffi

MSC:

76S05	Flows in porous media; filtration; seepage
76M99	Basic methods in fluid mechanics

Keywords:

finite difference scheme; Cauchy problem; approximate interfaces; vanishing viscosity term