Abstract
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 in [Mielke and Ortiz, ESAIM Control Optim. Calc. Var. 14: 494–516, 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 Γ-convergence (cf. [Anzellotti and Baldo, Appl. Math. Optim. 27: 195–123, 1993]) in the limit of vanishing viscosity.
© de Gruyter 2008
