Section: New Results

Control of approximation errors

Participants : Eléonore Gauci, Alain Dervieux, Adrien Loseille [Gamma3 team, Inria-Rocquencourt] , Frédéric Alauzet [Gamma3 team, Inria-Rocquencourt] , Anca Belme [university of Paris 6] , Gautier Brèthes [university of Montreal] , Alexandre Carabias [Lemma] .

Reducing approximation errors as much as possible is a particular kind of optimal control problem. We formulate it exactly this way when we look for the optimal metric of the mesh, which minimizes a user-specified functional (goal-oriented mesh adaptation). In that case, the usual methods of optimal control apply, using adjoint states that can be produced by Algorithmic Differentiation.

This year, two conference papers were written on the methods of the team, including new analyses in [11],[10], a work on correctors in CFD in an AIAA paper. A detailed study of adjoint-based mesh adaptation for Navier-Stokes flows has been completed and published in a journal [9].

Following participation of Gamma3 and Ecuador to the European project UMRIDA (ended 2017), we wrote chapters 20, 21, 45, and 48 of the book “Uncertainty Management for Robust Industrial Design in Aeronautics”, edited by C. Hirsch et al. in the Springer series Notes on Numerical Fluid Mechanics and Multidisciplinary Design (2019).