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