A hierarchical NXFEM for fictitious domain simulations

Roland Becker (1) , Erik Burman (2) , Peter Hansbo (3)

1 LMAP - Laboratoire de Mathématiques appliquées de Pau
2 IACS - CMCS - Institut d'Analyse et Calcul Scientifique [Lausanne]
3 Chalmers University of Technology [Göteborg]

We suggest a fictitious domain method, based on the Nitsche XFEM method in this paper, that employs a band of elements adjacent to the boundary. In contrast, the classical fictitious domain method uses Lagrange multipliers on a line (surface) where the boundary condition is to be enforced. The idea can be seen as an extension of the Chimera method (see this link), but with a hierarchical representation of the discontinuous solution field. The hierarchical formulation is better suited for moving fictitious boundaries since the stiffness matrix of the underlying structured mesh can be retained during the computations. Our technique allows for optimal convergence properties irrespective of the order of the underlying finite element method.

Mots clés: extended finite element method; fictitious domain; Nitsche's method

Domaines: Sciences de l'ingénieur [physics]

Roland Becker, Erik Burman, Peter Hansbo. A hierarchical NXFEM for fictitious domain simulations. International Journal for Numerical Methods in Engineering, 2011, 86 (4-5), pp.549-559. ⟨10.1002/nme.3093⟩. ⟨hal-01352895⟩