Publications on the XFEM

We have gathered some of the most important publications on the XFEM and related methods. For easier access we have sorted them into the following categories:

GFEM, PUFEM, PUM and other methods related to the XFEM

1 I. Babuška, J.M. Melenk: The partition of unity method, Internat. J. Numer. Methods Engrg., 40, 727–758, 1997.
2 C.A. Duarte, O.N. Hamzeh, T.J. Liszka, W.W. Tworzydlo: A generalized finite element method for the simulation of three-dimensional dynamic crack propagation, Comp. Methods Appl. Mech. Engrg., 190, 2227–2262, 2001.
3 C.A. Duarte, D.J. Kim: Analysis and applications of a generalized finite element method with global-local enrichment functions, Comp. Methods Appl. Mech. Engrg., 197, 487–504, 2008.
4 J.M. Melenk, I. Babuška: The partition of unity finite element method: basic theory and applications, Comp. Methods Appl. Mech. Engrg., 139, 289–314, 1996.
5 J.T. Oden, C.A.M. Duarte, O.C. Zienkiewicz: A new cloud-based hp finite element method, Comp. Methods Appl. Mech. Engrg., 153, 117–126, 1998.
6 A. Simone, C.A. Duarte, E. Van der Giessen: A generalized finite element method for polycrystals with discontinuous grain boundaries, Internat. J. Numer. Methods Engrg., 67, 1122–1145, 2006.
7 T. Strouboulis, K. Copps, I. Babuška: The generalized finite element method: an example of its implementation and illustration of its performance, Internat. J. Numer. Methods Engrg., 47, 1401–1417, 2000.
8 T. Strouboulis, I. Babuška, R. Hidajat: The generalized finite element method for Helmholtz equation: theory, computation, and open problems, Comp. Methods Appl. Mech. Engrg., 195, 4711–4731, 2006.
9 T. Strouboulis, R. Hidajat, I. Babuška: The generalized finite element method for Helmholtz equation, part II: effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment, Comp. Methods Appl. Mech. Engrg., 197, 364–380, 2008.

Thomas-Peter Fries (fries@tugraz.at)