(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Mielke, Alexander; Stefanelli, Ulisse
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.
