Adaptive approximation of the Monge–Kantorovich problem via primal-dual gap estimates
Bartels, Sören1 ; Schön, Patrick1
1 Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Str. 10, 79104 Freiburg i.Br., Germany.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2237-2261.

The Monge–Kantorovich problem arises as a special case for linear cost functionals in optimal transportation problems. It leads to a convex minimization problem with limited regularity properties. The convergent finite element discretization and iterative solution of the problem and its dual are addressed. Based on these approximations a computable upper bound for the primal-dual gap is derived which is suitable for efficient local mesh refinement. Numerical experiments reveal a significant improvement of related adaptive methods.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017054
Classification : 65K10, 65N50, 49M25, 90C08
Mots-clés : Optimal transport, a posteriori error estimation, iterative solution, adaptive mesh refinement
Bartels, Sören 1 ; Schön, Patrick 1

1 Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Str. 10, 79104 Freiburg i.Br., Germany. 
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Bartels, Sören; Schön, Patrick. Adaptive approximation of the Monge–Kantorovich problem via primal-dual gap estimates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2237-2261. doi : 10.1051/m2an/2017054. http://www.numdam.org/articles/10.1051/m2an/2017054/

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