Abstract
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.
Original language | English |
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Pages (from-to) | 201-238 |
Number of pages | 38 |
Journal | Interfaces and Free Boundaries |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2009 |
Keywords
- Augmented Lagrangian
- Convergence analysis
- Finite elements
- Free boundary
- Monge-Kantorovich problem
- Optimal transportation
- Variational formulation
ASJC Scopus subject areas
- Surfaces and Interfaces