Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An interface tracking algorithm for the porous medium equation


Authors: E. DiBenedetto and David Hoff
Journal: Trans. Amer. Math. Soc. 284 (1984), 463-500
MSC: Primary 65M10; Secondary 35K55, 35Q20, 35R35, 76S05
MathSciNet review: 743729
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the convergence of a finite difference scheme for the Cauchy problem for the porous medium equation $ {u_t} = {({u^m})_{x\,x}},m > 1$.

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. We thus generate approximate interfaces as well as an approximate solution.

The second feature is that it contains a vanishing viscosity term. This term permits an estimate of the form $ \parallel {({u^{m - 1}})_{x\,x}}\;\parallel _{1,{\mathbf{R}}} \leqslant c/t$.

We 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 65M10, 35K55, 35Q20, 35R35, 76S05

Retrieve articles in all journals with MSC: 65M10, 35K55, 35Q20, 35R35, 76S05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0743729-3
PII: S 0002-9947(1984)0743729-3
Article copyright: © Copyright 1984 American Mathematical Society