Séminaire d'analyse

A nonsmooth Brezzi-Rappaz-Raviart approximation theorem and application to mean field games
Jules Berry (Centrale Supélec Paris)
Thursday 12 November 2026 14:00 -  Tours -  E2290

Résumé :

The Brezzi-Rappaz-Raviart theorem is a quantitative version of
the inverse function theorem for analyzing numerical methods for
nonlinear PDEs. It provides conditions under which approximate problems
have solutions and bounds the error by the consistency error. Those
conditions rely on smoothness assumptions that many important problems
fail to satisfy. We extend the theorem to mere Lipschitz regularity,
using metric regularity in place of invertibility of derivatives. We
discuss applications to finite element approximations of Hamilton-Jacobi
equations and mean field games, where the nonlinearities are in general
not smooth enough for the classical theory.

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