A Mixed Formulation of the Monge-Kantorovich Equations
Mathematics, Imperial College London, London SW7 2AZ, UK. email@example.com
2 Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel.
Revised: 21 May 2007
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.
Mathematics Subject Classification: 35D05 / 35J85 / 49J40 / 65N12 / 65N30 / 82B27
Key words: Monge-Kantorovich problem / optimal transportation / mixed methods / finite elements / existence / convergence analysis.
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