Convergence order of a numerical scheme for sweeping process

Frederic Bernicot (1) , Juliette Venel (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to compactness arguments. Here we establish that this algorithm is of order 1/2 . The considered sweeping process involves a set-valued map given by a finite number of inequality constraints. The proof rests on a metric qualification condition between the sets associated to each constraint.

Mots clés: Differential inclusions; Subdifferential calculus; Numerical analysis; Prediction-correction algorithm

Domaines: Analyse numérique [math.NA]

Frederic Bernicot, Juliette Venel. Convergence order of a numerical scheme for sweeping process. SIAM Journal on Control and Optimization, 2013, 51 (4), pp.3075-3092. ⟨10.1137/120882044⟩. ⟨hal-00517485v2⟩