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:
S. Osher, R.P. Fedkiw:
Level set methods: an overview and some recent results,
J. Comput. Phys., 169, 463–502, 2001.
D. Peng, B. Merriman, S. Osher, H. Zhao, M. Kang:
A PDE-based fast local level set method,
J. Comput. Phys., 155, 410–438, 1999.
S.P. van der Pijl, A. Segal, C. Vuik, P. Wesseling:
A mass-conserving level-set method for modelling of multi-phase flows,
Int. J. Numer. Methods Fluids, 47, 339–361, 2005.
Fast marching methods,
SIAM Review, 41, 199–235, 1999.
Evolution, implementation and application of level set and fast marching methods for advancing fronts,
J. Comput. Phys., 169, 503–555, 2001.
M. Sussman, P. Smereka, S. Osher:
A level set approach for computing solutions to incompressible two-phase flow,
J. Comput. Phys., 114, 146–159, 1994.
M. Sussman, E. Fatemi:
An efficient interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow,
SIAM J. Sci. Comput., 20, 1165–1191, 1999.
G. Ventura, E. Budyn, T. Belytschko:
Vector level sets for description of propagating cracks in finite elements,
Internat. J. Numer. Methods Engrg., 58, 1571–1592, 2003.
H.K. Zhao, T. Chan, B. Merriman, S. Osher:
A variational level set approach to multiphase motion,
J. Comput. Phys., 127, 179–195, 1996.