A hierarchical NXFEM for fictitious domain simulations
Article first published online: 29 DEC 2010
Copyright © 2010 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Special Issue: Extended Finite Element Method
Volume 86, Issue 4-5, pages 549–559, 29 April - 6 May 2011
How to Cite
Becker, R., Burman, E. and Hansbo, P. (2011), A hierarchical NXFEM for fictitious domain simulations. Int. J. Numer. Meth. Engng., 86: 549–559. doi: 10.1002/nme.3093
- Issue published online: 28 MAR 2011
- Article first published online: 29 DEC 2010
- Manuscript Accepted: 26 OCT 2010
- Manuscript Revised: 6 OCT 2010
- Manuscript Received: 20 APR 2010
- Nitsche's method;
- fictitious domain;
- extended finite element method
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. Copyright © 2010 John Wiley & Sons, Ltd.