Section: New Results

Control of approximation errors

Participants : Alexandre Carabias, Gautier Brethes, Alain Dervieux, Adrien Loseille [Gamma3 team, Inria-Rocquencourt] , Frédéric Alauzet [Gamma3 team, Inria-Rocquencourt] , Estelle Mbinky [Gamma3 team, Inria-Rocquencourt] , Stephen Wornom [Lemma] , Olivier Allain [Lemma] , Anca Belme [university of Paris 6] .

Third-order mesh adaptation was the main topic of the year in error control. Two PhD have been completed this year on third-order mesh adaptation:

• In team Gamma3, Estelle Mbinky has studied a method from Bernard Mourrain for transforming trilinear Taylor terms of the approximation error into a power of a bilinear term. Estelle Mbinky defended her thesis at Paris 6 on december 20.

• In our team, Alexandre Carabias (who spent most of this year with team Gamma3) has developed a 2D third-order scheme for the Euler model. The scheme is based on the ENO finite-volume formulation with quadratic reconstruction. Some effort was devoted to improve the performance of the scheme. The scheme is much less dissipative than an usual quadratic ENO scheme and of smaller cost. Implementation of a 3D version in aironum (cf  5.1 ) is now starting. The 2D scheme has been the basis of an investigation of third order anisotropic mesh adaptation. Alexandre Carabias defended his thesis in Sophia-Antipolis on december 12.

A. Carabias and E. Mbinky presented their work on “A priori-based mesh adaptation for third-order accurate Euler simulation” at HONOM 2013, Bordeaux, France, March 18-22. We further studied mesh adaptation for viscous flows and we are preparing a journal article in collaboration with Gamma3 and University of Paris 6.

This year's new topic is the combination of Multi-Grid and anisotropic mesh adaption, with the starting PhD of Gautier Brèthes. The study involves several problematics, and in particular stopping criteria and construction of correctors. This was supported by the ANR project ECINADS, ended in november, but continues with the ANR project MAIDESC (started in october, coordinated by our team) following on mesh adaption and in particular meshes for interfaces, third-order accuracy, meshes for boundary layers, and curved meshes.