A hierarchical NXFEM for fictitious domain simulations
Journal article, 2011

We suggest a fictitious domain method, based on the Nitsche XFEM method of (Comput. Meth. Appl. Mech. Engrg 2002; 191: 5537-5552), 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 of (ESAIM: Math. Model Numer. Anal. 2003; 37: 495-514), 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.

Nitsche's method

extended finite element method

fictitious domain


nitsches method



R. Becker

Universite de Pau et des Pays de L'Adour

Erik Burman

University of Sussex

Peter F G Hansbo

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

International Journal for Numerical Methods in Engineering

0029-5981 (ISSN) 1097-0207 (eISSN)

Vol. 86 4-5 549-559

Subject Categories

Computational Mathematics



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9/6/2018 2