New bounding techniques for goal-oriented error estimation applied to linear problems

Pierre Ladevèze (1) , Florent Pled (1) , Ludovic Chamoin (1)

1 LMT - Laboratoire de Mécanique et Technologie

The paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method. A considerable improvement is introduced for linear problems thanks to new bounding techniques based on Saint-Venant's principle. The main breakthrough of these optimized bounding techniques is the use of properties of homothetic domains which enables to cleverly derive guaranteed and accurate boundings of contributions to the global error estimate over a local region of the domain. Performances of these techniques are illustrated through several numerical experiments.

Mots clés: finite element method; goal-oriented error estimation; Saint-Venant's principle; guaranteed error bounds; verification

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Pierre Ladevèze, Florent Pled, Ludovic Chamoin. New bounding techniques for goal-oriented error estimation applied to linear problems. International Journal for Numerical Methods in Engineering, 2013, 93 (13), pp.1345-1380. ⟨10.1002/nme.4423⟩. ⟨hal-01056891v2⟩