Section: New Results

Control of approximation errors

Participants : Alain Dervieux, Loic Frazza [Gamma3 team, Inria-Saclay] , Adrien Loseille [Gamma3 team, Inria-Saclay] , Frédéric Alauzet [Gamma3 team, Inria-Saclay] , Anca Belme [university of Paris 6] , 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, we published the final revised versions of two conference papers [23], [21], we published in a journal the final version of the adjoint-based mesh adaptation for Navier-Stokes flows [16]), and we published in “Numerical Methods in Fluids” a work on nonlinear correctors extending [22]. Let us also mention the final publication 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) in which we have contributed chapters 20, 21, 45, and 48.

The monography on mesh adaptation currently being written by Alauzet, Loseille, Koobus and Dervieux now involves all its chapters (14 chapters) and is being finalized.