# Approximation of Parabolic Equations Using the Wasserstein Metric

David Kinderlehrer; Noel J. Walkington

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 4, page 837-852
- ISSN: 0764-583X

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topKinderlehrer, David, and Walkington, Noel J.. "Approximation of Parabolic Equations Using the Wasserstein Metric." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 837-852. <http://eudml.org/doc/197465>.

@article{Kinderlehrer2010,

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.
},

author = {Kinderlehrer, David, Walkington, Noel J.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Wasserstein metric; parabolic equations; numerical
approximations.; variational method; parabolic initial-boundary value problems; time discretization; convection-diffusion equations; Fokker-Planck equation; heat equation; Stefan problem},

language = {eng},

month = {3},

number = {4},

pages = {837-852},

publisher = {EDP Sciences},

title = {Approximation of Parabolic Equations Using the Wasserstein Metric},

url = {http://eudml.org/doc/197465},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Kinderlehrer, David

AU - Walkington, Noel J.

TI - Approximation of Parabolic Equations Using the Wasserstein Metric

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 4

SP - 837

EP - 852

AB -
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.

LA - eng

KW - Wasserstein metric; parabolic equations; numerical
approximations.; variational method; parabolic initial-boundary value problems; time discretization; convection-diffusion equations; Fokker-Planck equation; heat equation; Stefan problem

UR - http://eudml.org/doc/197465

ER -

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