Juliette Venel

Learn More
We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We further show that a similar property holds for the discrete problem for any regular meshes, extending the framework from(More)
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the(More)
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We limit our approach to very basic principles in terms of behavior, to focus on the particular problems raised by the(More)
2 Mathematical framework and well-posedness results 4 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Uniform prox-regularity of sets Q(t) . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Lipschitz regularity of Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Well-posedness(More)
Abstract In [19], 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(More)
This paper is devoted to weaken “classical” assumptions and give new arguments to prove existence of sweeping process (associated to the proximal normal cone of sets). Mainly we define the concept of a “directional prox-regularity” and give assumptions about a Banach space to insure the existence of such sweeping process (which permit to generalize the(More)
The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by a uniformly prox-regular set. After obtaining well-posedness results, we propose a numerical scheme based on a predictioncorrection algorithm and we prove its convergence. Finally we apply these results to a(More)