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A hierarchical NXFEM for fictitious domain simulations
journal contribution
posted on 2023-06-07, 20:55 authored by Roland Becker, Erik Burman, Peter HansboWe 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.
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Publication status
- Published
Journal
International Journal for Numerical Methods in EngineeringISSN
00295981External DOI
Issue
4-5Volume
86Page range
549-559Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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