A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal for Numerical Methods in Engineering Année : 2009

A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method

Résumé

This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier approaches. we do not work with an interior penalty formulation as, e.g. for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. Roughly speaking a stable and optimal discrete Lagrange multiplier space has to satisfy two criteria: a best approximation property and a uniform inf-sup condition. Owing to the fact that the interface does not match the edges of the mesh, the choice of a good discrete Lagrange Multiplier space is not trivial. Here we propose a new algorithm for the local construction of the Lagrange Multiplier space and show that a uniform inf-sup condition is satisfied. A counterexample is also presented, i.e. the inf-sup constant depends on the mesh-size and degenerates as it tends to zero. Numerical results in two-dimensional confirm the theoretical ones.
Fichier principal
Vignette du fichier
Bechet2008.pdf (462.61 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01004951 , version 1 (05-02-2023)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

Citer

Eric Béchet, Nicolas Moes, Barbara Wohlmuth. A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. International Journal for Numerical Methods in Engineering, 2009, 78 (8), pp.931-954. ⟨10.1002/nme.2515⟩. ⟨hal-01004951⟩
114 Consultations
37 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More