A hierarchical NXFEM for fictitious domain simulations

Becker, Roland, Burman, Erik and Hansbo, Peter (2011) A hierarchical NXFEM for fictitious domain simulations. International Journal for Numerical Methods in Engineering, 86 (4-5). pp. 549-559. ISSN 00295981

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 18:40
Last Modified: 03 Apr 2012 13:36
URI: http://sro.sussex.ac.uk/id/eprint/17681
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