Accession Number : ADA127685


Title :   An Interface Tracking Algorithm for the Porous Medium Equation.


Descriptive Note : Technical summary rept.,


Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER


Personal Author(s) : DiBenedetto,E ; Hoff,D C


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a127685.pdf


Report Date : Mar 1983


Pagination or Media Count : 90


Abstract : The authors study the convergence of a finite difference scheme for the Cauchy problem for a porous medium equation. The scheme exhibits the following two features. The first is that it employs a discretization of the known interface condition for the propagation of the support of the solution. Thus generated are approximate interfaces as well as an approximate solution. The second feature is that it contains a vanishing viscosity term. The authors prove that both the approximate solution and the approximate interfaces converge to the correct ones. Finally error bounds for both solution and free boundaries are proved in terms of the mesh parameters.


Descriptors :   *ALGORITHMS , *DIFFERENCE EQUATIONS , *GAS FLOW , *CAUCHY PROBLEM , INTERFACES , PROBLEM SOLVING , MESH , ESTIMATES , FINITE DIFFERENCE THEORY , APPROXIMATION(MATHEMATICS) , BOUNDARY VALUE PROBLEMS , ERRORS , CONVERGENCE


Subject Categories : Theoretical Mathematics
      Fluid Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE