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Approximation of Parabolic Equations Using 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 be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into 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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