A discrete variational principle for rate-independent evolution
- Mielke, Alexander
- Stefanelli, Ulisse
2010 Mathematics Subject Classification
- 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.
- Adv. Calculus Variations, 1 (2008) pp. 399--431.