Convergence order of a numerical scheme for sweeping process

TL;DR

This paper proves that a previously introduced numerical scheme for sweeping processes converges with an order of 1/2, under certain qualification conditions, improving understanding of its numerical accuracy.

Contribution

It establishes the convergence order of the numerical scheme for sweeping processes, providing theoretical validation of its rate of convergence.

Findings

The scheme converges with order 1/2.

Convergence proof relies on a metric qualification condition.

The algorithm is implementable for differential inclusions with inequality constraints.

Abstract

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.