A mixed formulation of the Monge-Kantorovich equations

John W. Barrett; Leonid Prigozhin

doi:10.1051/m2an:2007051

A mixed formulation of the Monge-Kantorovich equations

John W. Barrett, Leonid Prigozhin

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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.

Original language	English
Pages (from-to)	1041-1060
Number of pages	20
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	41
Issue number	6
DOIs	https://doi.org/10.1051/m2an:2007051
State	Published - 1 Nov 2007

Keywords

Convergence analysis
Existence
Finite elements
Mixed methods
Monge-Kantorovich problem
Optimal transportation

ASJC Scopus subject areas

Analysis
Numerical Analysis
Modeling and Simulation
Computational Mathematics
Applied Mathematics

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10.1051/m2an:2007051

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AB - 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.

KW - Convergence analysis

KW - Existence

KW - Finite elements

KW - Mixed methods

KW - Monge-Kantorovich problem

KW - Optimal transportation

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ER -

A mixed formulation of the Monge-Kantorovich equations

Abstract

Keywords

ASJC Scopus subject areas

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