Geodesic
The Discrete Brezis-Ekeland Principle
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 71-87

Voir la notice de l'article provenant de la source Heldermann Verlag

We discuss a global-in-time variational approach to the time-discretization of gradient flows of convex functionals in Hilbert spaces. In particular, a discrete version of the celebrated Brezis-Ekeland variational principle is considered. The variational principle consists in the minimization of a functional on entire time-discrete trajectories. The latter functional admits a unique minimizer which solves the classical backward Euler scheme. This variational characterization is exploited in order to re-obtain in a variational fashion and partly extend the known convergence analysis for the Euler method. The relation between this variational technique and a posteriori error control and space approximation is also discussed.
Classification : 35K55
Mots-clés : Gradient flow, Euler method, Brezis-Ekeland principle, convergence, error control 
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     author = {U. Stefanelli},
     title = {The {Discrete} {Brezis-Ekeland} {Principle}},
     journal = {Journal of convex analysis},
     pages = {71--87},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a3/}
}
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U. Stefanelli. The Discrete Brezis-Ekeland Principle. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 71-87. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a3/