Premium
The extended finite element method (XFEM) for solidification problems
Author(s) -
Chessa Jack,
Smolinski Patrick,
Belytschko Ted
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.386
Subject(s) - extended finite element method , discontinuity (linguistics) , finite element method , mixed finite element method , robustness (evolution) , interface (matter) , finite element limit analysis , basis function , mathematics , mathematical analysis , computer science , mathematical optimization , structural engineering , engineering , biochemistry , chemistry , bubble , maximum bubble pressure method , parallel computing , gene
Abstract An enriched finite element method for the multi‐dimensional Stefan problems is presented. In this method the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface. The approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element. The phase interface can be evolved without re‐meshing or the use of artificial heat capacity techniques. The interface is described by a level set function that is updated by a stabilized finite element scheme. Several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method. Copyright © 2001 John Wiley & Sons, Ltd.