Section: New Results

Control of approximation errors

Participants : Gautier Brèthes, Eléonore Gauci, Alain Dervieux, Adrien Loseille [GAMMA team, Inria-Rocquencourt] , Frédéric Alauzet [GAMMA team, Inria-Rocquencourt] , Stephen Wornom [Lemma] , Anca Belme [university of Paris 6] .

The study of combination of full multigrid (FMG) with anisotropic mesh adaption (AA), started with the thesis of Gautier Brèthes, has been published [13] .

Further studies of mesh adaptation for viscous flows are currently performed and a journal paper, joint with Inria team Gamma3 and University of Paris 6 (Anca Belme) is in preparation.

An important novelty in mesh adaption is the norm-oriented AA method. The method relies on the definition of ad hoc correctors. It has been developed in the academic platform “FMG" for elliptic problems. Gautier Brèthes gave several presentations in conferences, a journal article has been submitted. The introduction of the norm-oriented idea considerably amplifies the impact of adjoint-based AA. The applied mathematician and the engineer now have methods when faced to mesh adaptation for the simulation of a complex PDE system, since they can specify which error norm level they wish, and for which norm [12] , [16] . Another version is developed jointly with Inria team Gamma3 for the compressible Euler model [19] .

A cooperation has started between Gautier Brèthes et Thierry Coupez (Ecole Centrale de Nantes) concerning discrete metrics. This takes place in the ANR MAIDESC program. An article is in preparation.

Éléonore Gauci started last year a thesis (co-advised by Frédéric Alauzet) on the study of norm-oriented criteria for CFD and coupled CSM-CFD systems. She gave a presentation at the “Coupled Problems" symposium.

Post-doc Guilherme Cunha did a study (in cooperation with Lemma) on the combination of mesh adaptation and coefficient identification for unsteady phenomena.

The theoretical studies are supported by an ANR project MAIDESC coordinated by ECUADOR and Gamma3, which deals with meshes for interfaces, third-order accuracy, meshes for boundary layers, and curved meshes.

CFD application are supported by the European FP7 project UMRIDA which deals with the application of AA to approximation error modelling and control.