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A Mixed Formulation of the Monge-Kantorovich Equations

Published online by Cambridge University Press:  15 December 2007

John W. Barrett  and
Leonid Prigozhin
John W. Barrett
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK. jwb@ic.ac.uk
Leonid Prigozhin
Affiliation:
Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel.
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Abstract

We introduce and analyse a mixed formulation of theMonge-Kantorovich equations, which express optimality conditions forthe mass transportation problem with cost proportional to distance.Furthermore, we introduce and analyse the finite elementapproximation of this formulation using the lowest orderRaviart-Thomas element. Finally, we present some numericalexperiments, where both the optimal transport density and theassociated Kantorovich potential are computed for a coupling problemand problems involving obstacles and regions of cheaptransportation.

Keywords

Monge-Kantorovich problemoptimal transportationmixed methodsfinite elementsexistenceconvergence analysis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 6 , November 2007 , pp. 1041 - 1060
Copyright
© EDP Sciences, SMAI, 2007

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