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.
Accepté le :
DOI : 10.1051/m2an/2017054
Mots clés : Optimal transport, a posteriori error estimation, iterative solution, adaptive mesh refinement
@article{M2AN_2017__51_6_2237_0, author = {Bartels, S\"oren and Sch\"on, Patrick}, title = {Adaptive approximation of the {Monge{\textendash}Kantorovich} problem via primal-dual gap estimates}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {2237--2261}, publisher = {EDP-Sciences}, volume = {51}, number = {6}, year = {2017}, doi = {10.1051/m2an/2017054}, mrnumber = {3745171}, zbl = {1396.65100}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2017054/} }
TY - JOUR AU - Bartels, Sören AU - Schön, Patrick TI - Adaptive approximation of the Monge–Kantorovich problem via primal-dual gap estimates JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 2237 EP - 2261 VL - 51 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017054/ DO - 10.1051/m2an/2017054 LA - en ID - M2AN_2017__51_6_2237_0 ER -
%0 Journal Article %A Bartels, Sören %A Schön, Patrick %T Adaptive approximation of the Monge–Kantorovich problem via primal-dual gap estimates %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 2237-2261 %V 51 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017054/ %R 10.1051/m2an/2017054 %G en %F M2AN_2017__51_6_2237_0
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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