Volume 51, Number 6, November-December 2017
|Page(s)||2237 - 2261|
|Published online||12 December 2017|
Adaptive approximation of the Monge–Kantorovich problem via primal-dual gap estimates
Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Str. 10, 79104 Freiburg i.Br., Germany.
Received: 21 March 2017
Revised: 26 October 2017
Accepted: 5 November 2017
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.
Mathematics Subject Classification: 65K10 / 65N50 / 49M25 / 90C08
Key words: Optimal transport / a posteriori error estimation / iterative solution / adaptive mesh refinement
© EDP Sciences, SMAI 2017
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