An Interface Tracking Algorithm for the Porous Medium Equation.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
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.
- Theoretical Mathematics
- Fluid Mechanics