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Approximation of Parabolic EquationsUsing the Wasserstein Metric

Published online by Cambridge University Press:  15 August 2002

David Kinderlehrer  and
Noel J. Walkington
David Kinderlehrer
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Supported in part by ARO DAAH Grant 04 96 0060, NSF Grant DMS–9505078.
Noel J. Walkington
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Supported in part by NSF Grant DMS–9504492.
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Abstract

We illustrate how some interesting new variational principles can beused for the numerical approximation of solutions to certain (possiblydegenerate) parabolic partial differential equations. One remarkablefeature of the algorithms presented here is that derivatives do notenter into the variational principles, so, for example, discontinuousapproximations may be used for approximating the heat equation. Wepresent formulae for computing a Wasserstein metric which entersinto the variational formulations.

Keywords

Wasserstein metricparabolic equationsnumerical approximations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 4 , July 1999 , pp. 837 - 852
Copyright
© EDP Sciences, SMAI, 1999

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