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:

The level-set method

1 S. Osher, R.P. Fedkiw: Level set methods: an overview and some recent results, J. Comput. Phys., 169, 463–502, 2001.
2 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.
3 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.
4 J.A. Sethian: Fast marching methods, SIAM Review, 41, 199–235, 1999.
5 J.A. Sethian: Evolution, implementation and application of level set and fast marching methods for advancing fronts, J. Comput. Phys., 169, 503–555, 2001.
6 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.
7 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.
8 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.
9 H.K. Zhao, T. Chan, B. Merriman, S. Osher: A variational level set approach to multiphase motion, J. Comput. Phys., 127, 179–195, 1996.

Thomas-Peter Fries (fries@tugraz.at)