David Kinderlehrer and Noel J. Walkington
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213
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.
Key Words. Wasserstein Metric, Parabolic Equations, Numerical Approximations
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