Andreas Byfut
,
Andreas Schröder
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),
MSC 2000
- 74S05 Finite element methods
-
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Abstract
This paper discusses higher-order extended finite element methods obtained from the combination of the standard extended finite element method (XFEM) with higher-order finite element methods. Here, the focus is on the embedding of the latter into the partition of unity method, which is the basis of the XFEM. A priori error estimates are discussed and numerical verifi cation is given for two benchmark problems. Moreover, methodological aspects are summarized which are necessary for hp-adaptivity in XFEM and allow for exponential convergence rates. In particular, the handling of hanging nodes via constraint approximation and an hp-adaptive strategy are presented.
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