TY  - JOUR
N1  - 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.
KW  - Nitsche's method
KW  -  fictitious domain
KW  -  extended finite element method
SN  - 0029-5981
TI  - A hierarchical NXFEM for fictitious domain simulations
AV  - public
IS  - 4-5
EP  -  559
VL  - 86
SP  - 549 
A1  - Becker, R
A1  - Burman, E
A1  - Hansbo, P
JF  - International Journal for Numerical Methods in Engineering
Y1  - 2011/04/29/
N2  - 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.
ID  - discovery1384750
UR  - http://dx.doi.org/10.1002/nme.3093
ER  -