WIAS Preprint No. 1295, (2008)

A discrete variational principle for rate-independent evolution


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Stefanelli, Ulisse

2010 Mathematics Subject Classification

  • 35K55


  • Variational Principle, rate-independent process, time-discretization




We develop a global-in-time variational approach to the time-discretization of rate-independent processes. In particular, we investigate a discrete version of the variational principle based on the weighted energy-dissipation functional introduced by A. Mielke and M. Ortiz in ESAIM Control Optim. Calc. Var., 2008. We prove the conditional convergence of time-discrete approximate minimizers to energetic solutions of the time-continuous problem. Moreover, the convergence result is combined with approximation and relaxation. For a fixed partition the functional is shown to have an asymptotic development by Gamma convergence, cf. G. Anzellotti and S. Baldo (Appl. Math. Optim., 1993), in the limit of vanishing viscosity.

Appeared in

  • Adv. Calculus Variations, 1 (2008) pp. 399--431.

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