Thumbnail

φ-FEM, a finite element method on domains defined by level-sets: the Neumann boundary case

Duprez, Michel; Lleras, Vanessa; Lozinski, Alexei (2020), φ-FEM, a finite element method on domains defined by level-sets: the Neumann boundary case. https://basepub.dauphine.fr/handle/123456789/20597

View/Open
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02521042
Date
2020
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
24
Metadata
Show full item record
Author(s)
Duprez, Michel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lleras, Vanessa
Institut Montpelliérain Alexander Grothendieck [IMAG]
Lozinski, Alexei
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Abstract (EN)
We extend a fictitious domain-type finite element method, called φ-FEM and introduced in [7], to the case of Neumann boundary conditions. The method is based on a multiplication by the level-set function and does not require a boundary fitted mesh. Unlike other recent fictitious domain-type methods (XFEM, CutFEM), our approach does not need any non-standard numerical integration on cut mesh elements or on the actual boundary. We prove the optimal convergence of φ-FEM and the fact that the discrete problem is well conditioned inependently of the mesh cuts. The numerical experiments confirm the theoretical results.
Subjects / Keywords
Finite element method; fictitious domain; level-set; Neumann conditions