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.

Our theoretical studies in mesh adaptation are supported by the ANR project MAIDESC coordinated by ECUADOR and Gamma3, which deals with meshes for interfaces, third-order accuracy, meshes for boundary layers, and curved meshes.

During this year, two works, one on the tensorial metric method started during the thesis of Gautier Brèthes [12], and one on mesh adaptation for third order approximation [13], were completed and published in journals.

Further studies of mesh adaptation for viscous flows are currently performed and a paper in collaboration with Gamma3 and university of Paris 6 (Anca Belme) has been submitted to a Journal.