General One-Phase Stefan Problems and Free Boundary Problems for the Heat Equation with Cauchy Data Prescribed on the Free Boundary

1971 ◽  
Vol 20 (4) ◽  
pp. 555-570 ◽  
Author(s):  
B. Sherman
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Free Boundary Problems ◽  
Cauchy Data ◽  
Boundary Problems ◽  
Stefan Problems

scholarly journals General free-boundary problems for the heat equation, III

1977 ◽  
Vol 59 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Antonio Fasano ◽  
Mario Primicerio
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Free Boundary Problems ◽  
Boundary Problems

A Four-Step Fixed-Grid Method for 1D Stefan Problems

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Free Boundary Problems ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Stefan Problems ◽  
Fixed Grid

This note is concerned with a fixed-grid finite difference method for the solution of one-dimensional free boundary problems. The method solves for the field variables and the location of the boundary in separate steps. As a result of this decoupling, the nonlinear part of the algorithm involves only a scalar unknown, which is the location of the moving boundary. A number of examples are used to study the applicability of the method. The method is particularly useful for moving boundary problems with various conditions at the front.

scholarly journals General free-boundary problems for the heat equation, I

1977 ◽  
Vol 57 (3) ◽  
pp. 694-723 ◽  
Author(s):  
A Fasano ◽  
M Primicerio
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Free Boundary Problems ◽  
Boundary Problems

General free-boundary problems for the heat equation, II

1977 ◽  
Vol 58 (1) ◽  
pp. 202-231 ◽  
Author(s):  
Antonio Fasano ◽  
Mario Primicerio
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Free Boundary Problems ◽  
Boundary Problems

scholarly journals Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

2014 ◽  
Vol 15 (2) ◽  
pp. 506-555 ◽  
Author(s):  
John W. Barrett ◽  
Harald Garcke ◽  
Robert Nürnberg
Keyword(s):  
Free Boundary ◽  
Phase Field ◽  
Free Boundary Problems ◽  
Benchmark Problems ◽  
Computationally Efficient ◽  
Boundary Problems ◽  
Stefan Problems ◽  
Phase Field Models ◽  
Phase Field System ◽  
Anisotropic Phase

AbstractWe critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Here we focus on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.

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