Abstract

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.

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Keywords

  • Gradient flow
  • Euler method
  • Brezis-Ekeland principle
  • convergence
  • error control

Mathematics Subject Classification

35K55

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Suggested citation

U. Stefanelli. “The Discrete Brezis-Ekeland Principle.” Journal of Convex Analysis 16 (2009), No. 1, 71–87. https://doi.org/10.68381/jca16004

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.