Towards a robust and effective strategy for the control of finite element computations in mechanical engineering
type: Dataset
description: This research work aims at contributing to the development of innovative global and goal-oriented error estimation tools applied to Computational Mechanics. The global error estimators considered rely on the concept of constitutive relation error through specific techniques for constructing admissible fields ensuring the recovery of strict and high-quality error estimates. A new hybrid method for constructing admissible stress fields is set up and compared to two other techniques with respect to three different criteria, namely the quality of associated error estimators, the computational cost and the simplicity of practical implementation into finite element codes. An enhanced version of this new technique based on local minimization of the complementary energy is also proposed. Judicious geometric and energetic criteria are introduced to select the relevant zones for optimizing the quality of the admissible fields locally. In the context of goal-oriented error estimation based on the use of both extraction techniques and global error estimators, two new improved bounding techniques are proposed. They lean on Saint-Venant's principle through specific homotheticity properties in order to obtain guaranteed and relevant bounds of better quality than with the classical bounding technique based on the Cauchy-Schwarz inequality. The various comparative studies are conducted on linear elasticity problems under quasi-static loading conditions. The behaviour of the different error estimators is illustrated and discussed through several numerical experiments carried out on industrial cases. The associated results may open up opportunities and help broaden the field of model verification for both academic research and industrial applications.
identifier: NNT: 2012DENS0083
issued: 2026-05-12T06:24:42.180212
language: fr
modified: 2026-05-12T06:24:42.180218
contact point: Organization
  fn: CCSD
keyword: a-posteriori-error-estimation
keyword: admissible-fields
keyword: bornes-derreur-garanties
keyword: champs-admissibles
keyword: constitutive-relation-error
keyword: erreur-en-relation-de-comportement
keyword: estimation-derreur-a-posteriori
keyword: estimation-derreur-en-quantite-dinteret
keyword: finite-element-method
keyword: goal-oriented-error-estimation
keyword: guaranteed-error-bounds
keyword: infoeu-reposemanticsdoctoralthesis
keyword: methode-des-elements-finis
keyword: non-intrusive-techniques
keyword: principe-de-saint-venant
keyword: saint-venants-principle
keyword: spiotherengineering-sciences-physicsother
keyword: techniques-non-intrusives
keyword: theses
keyword: verification
landing page: https://theses.hal.science/tel-00776633

Towards a robust and effective strategy for the control of finite element computations in mechanical engineering
type: Distribution
format: HTML
issued: 2026-05-12T06:24:42.281137
modified: 2026-05-12T06:24:42.142729
access URL: https://theses.hal.science/tel-00776633

test_moissonnage_selune
type: Agent