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A hierarchical NXFEM for fictitious domain simulations

Becker, R; Burman, E; Hansbo, P; (2011) A hierarchical NXFEM for fictitious domain simulations. International Journal for Numerical Methods in Engineering , 86 (4-5) 549 - 559. 10.1002/nme.3093. Green open access

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Abstract

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.

Type: Article
Title: A hierarchical NXFEM for fictitious domain simulations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1002/nme.3093
Publisher version: http://dx.doi.org/10.1002/nme.3093
Language: English
Additional information: This is the peer reviewed version of the following article: Becker, R; Burman, E; Hansbo, P; (2011) A hierarchical NXFEM for fictitious domain simulations. International Journal for Numerical Methods in Engineering, 86 (4-5) pp. 549-559. 10.1002/nme.3093, which has been published in final form at http://dx.doi.org/10.1002/nme.3093. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Keywords: Nitsche's method, fictitious domain, extended finite element method
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1384750
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