New bounding techniques for goal-oriented error estimation in FE simulations

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

1 LMT - Laboratoire de Mécanique et Technologie

In this work, we propose new bounding techniques that enable to derive accurate and strict error bounds on outputs of interest computed from numerical ap- proximation methods such as the finite element method. These techniques are based on Saint-Venant's principle and exploit specific homotheticity properties in order to im- prove the quality of the bounds computed from the classical bounding technique. The capabilities of the proposed approaches are illustrated through two-dimensional numerical experiments carried out on a linear elasticity problem.

Mots clés: Non-intrusive Techniques; Saint-Venant's principle; Guaranteed Error Bounds; Constitutive relation error; Goal-oriented error estimation; Verification; Finite Element Method

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

Florent Pled, Ludovic Chamoin, Pierre Ladevèze. New bounding techniques for goal-oriented error estimation in FE simulations. 6th International Conference on Adaptive Modeling and Simulation (ADMOS 2013), Jun 2013, Lisbon, Portugal. pp.528-539. ⟨hal-01056926⟩