Toward alternative bounding techniques for robust goal-oriented error estimation applied to linear problems

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

1 LMT - Laboratoire de Mécanique et Technologie

In this work, we propose appealing bounding techniques that enable to derive accurate and strict error bounds on outputs of interest computed from numerical approximation methods such as the finite element method. These techniques are based on Saint-Venant's principle and exploit specific homotheticity properties in order to improve 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: finite element method; guaranteed error bounds; constitutive relation error; goal-oriented error estimation; Verification; homotheticity properties; Saint-Venant's principle

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

Florent Pled, Ludovic Chamoin, Pierrre Ladevèze. Toward alternative bounding techniques for robust goal-oriented error estimation applied to linear problems. 2nd ECCOMAS Young Investigators Conference (YIC 2013), Sep 2013, Bordeaux, France. ⟨hal-01057085⟩