scholarly journals The birth of a cusp in the two-dimensional, undercooled Stefan problem

2000 ◽  
Vol 58 (3) ◽  
pp. 473-494 ◽  
Author(s):  
M. A. Herrero ◽  
E. Medina ◽  
J. J. L. Velázquez
Keyword(s):  
Stefan Problem ◽  
Two Dimensional

Regularization of a two-dimensional two-phase inverse Stefan problem

1997 ◽  
Vol 13 (3) ◽  
pp. 607-619 ◽  
Author(s):  
D D Ang ◽  
A Pham Ngoc Dinh ◽  
D N Thanh
Keyword(s):  
Stefan Problem ◽  
Two Dimensional ◽  
Two Phase

A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

1998 ◽  
Vol 141 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Guus Segal ◽  
Kees Vuik ◽  
Fred Vermolen
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Two Dimensional

A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

2013 ◽  
Vol 5 (06) ◽  
pp. 825-845 ◽  
Author(s):  
B. Tomas Johansson ◽  
Daniel Lesnic ◽  
Thomas Reeve
Keyword(s):  
Stefan Problem ◽  
Regularization Method ◽  
Input Data ◽  
Stable Solution ◽  
Higher Dimensions ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Two Dimensional ◽  
Two Phase ◽  
Ill Posed

AbstractIn this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.

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