An Interface Tracking Algorithm for the Porous Medium Equation.

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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1983
Accession Number
ADA127685

Entities

People

  • D. C. Hoff
  • E. Dibenedetto

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Cauchy Problem
  • Computations
  • Contracts
  • Convergence
  • Difference Equations
  • Differential Equations
  • Equations
  • Inequalities
  • Integrals
  • Interpolation
  • Mathematics
  • Numerical Analysis
  • Theorems
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)