Approximation of Parabolic Equations Using the Wasserstein Metric
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.
2 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Supported in part by NSF Grant DMS–9504492.
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.
Mathematics Subject Classification: 65M60 / 49R10
Key words: Wasserstein metric / parabolic equations / numerical approximations.
© EDP Sciences, SMAI, 1999