DiBenedetto, E.; Hoff, David An interface tracking algorithm for the porous medium equation. (English) Zbl 0564.76090 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 Cited in 1 ReviewCited in 16 Documents 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 PDF BibTeX XML Cite \textit{E. DiBenedetto} and \textit{D. Hoff}, Trans. Am. Math. Soc. 284, 463--500 (1984; Zbl 0564.76090) Full Text: DOI