# A Mixed Formulation of the Monge-Kantorovich Equations

John W. Barrett; Leonid Prigozhin

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 6, page 1041-1060
- ISSN: 0764-583X

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topBarrett, John W., and Prigozhin, Leonid. "A Mixed Formulation of the Monge-Kantorovich Equations." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1041-1060. <http://eudml.org/doc/250035>.

@article{Barrett2007,

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.
},

author = {Barrett, John W., Prigozhin, Leonid},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Monge-Kantorovich problem; optimal transportation;
mixed methods; finite elements; existence;
convergence analysis.; mixed methods; convergence analysis},

language = {eng},

month = {12},

number = {6},

pages = {1041-1060},

publisher = {EDP Sciences},

title = {A Mixed Formulation of the Monge-Kantorovich Equations},

url = {http://eudml.org/doc/250035},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Barrett, John W.

AU - Prigozhin, Leonid

TI - A Mixed Formulation of the Monge-Kantorovich Equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/12//

PB - EDP Sciences

VL - 41

IS - 6

SP - 1041

EP - 1060

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.

LA - eng

KW - Monge-Kantorovich problem; optimal transportation;
mixed methods; finite elements; existence;
convergence analysis.; mixed methods; convergence analysis

UR - http://eudml.org/doc/250035

ER -

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