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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 the Monge-Kantorovich equations, which express optimality conditions for the mass transportation problem with cost proportional to distance. Furthermore, we introduce and analyse the finite element approximation of this formulation using the lowest order Raviart-Thomas element. Finally, we present some numerical experiments, where both the optimal transport density and the associated Kantorovich potential are computed for a coupling problem and problems involving obstacles and regions of cheap transportation.

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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