%0 Journal Article %1 noauthororeditor %A Chessa, Jack %A Smolinski, Patrick %A Belytschko, Ted %D 2002 %J International Journal for Numerical Methods in Engineering %K 80a22-stefan-problems-phase-changes-etc 80m10-heat-transfer-finite-element-methods %N 8 %P 1959-1977 %R 10.1002/nme.386 %T The extended finite element method (XFEM) for solidification problems %U https://www.onlinelibrary.wiley.com/doi/abs/10.1002/nme.386 %V 53 %X 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.

@article{noauthororeditor, 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. }, added-at = {2020-06-02T03:09:45.000+0200}, author = {Chessa, Jack and Smolinski, Patrick and Belytschko, Ted}, biburl = {https://www.bibsonomy.org/bibtex/253ebb2069ff9bdbdfb7faa6bbd4740a3/gdmcbain}, doi = {10.1002/nme.386}, interhash = {90dda6cdc593d348e8647f3939a6b00f}, intrahash = {53ebb2069ff9bdbdfb7faa6bbd4740a3}, journal = {International Journal for Numerical Methods in Engineering}, keywords = {80a22-stefan-problems-phase-changes-etc 80m10-heat-transfer-finite-element-methods}, number = 8, pages = {1959-1977}, timestamp = {2020-06-02T03:09:45.000+0200}, title = {The extended finite element method (XFEM) for solidification problems}, url = {https://www.onlinelibrary.wiley.com/doi/abs/10.1002/nme.386}, volume = 53, year = 2002 }