- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2009
2
Partial L1 Monge–Kantorovich problem: variational formulation and numerical approximation
John
Barrett
Imperial College London, LONDON, UNITED KINGDOM
Leonid
Prigozhin
Ben Gurion University of the Negev, BEER-SHEBA, ISRAEL
Monge–Kantorovich problem, optimal transportation, free boundary, variational formulation, finite elements, augmented Lagrangian, convergence analysis
We consider the Monge–Kantorovich problem with transportation cost equal to distance and a relaxed mass balance condition: instead of optimally transporting one given distribution of mass onto another with the same total mass, only a given amount of mass, m, has to be optimally transported. In this partial problem the given distributions are allowed to have different total masses and m should not exceed the least of them. We derive and analyze a variational formulation of the arising free boundary problem in optimal transportation. 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 approximations to the optimal transportation domains and the optimal transport between them are computed.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
201
238
10.4171/IFB/209
http://www.ems-ph.org/doi/10.4171/IFB/209