Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

1997 ◽  
Vol 77 (1) ◽  
pp. 1-34 ◽  
Author(s):  
John W. Barrett ◽  
James F. Blowey
Keyword(s):  
Finite Element ◽  
Free Energy ◽  
Phase Separation ◽  
Finite Element Approximation ◽  
Element Approximation

FINITE ELEMENT APPROXIMATION OF A MODEL FOR PHASE SEPARATION OF A MULTI-COMPONENT ALLOY WITH NONSMOOTH FREE ENERGY AND A CONCENTRATION DEPENDENT MOBILITY MATRIX

1999 ◽  
Vol 09 (05) ◽  
pp. 627-663 ◽  
Author(s):  
JOHN W. BARRETT ◽  
JAMES F. BLOWEY
Keyword(s):  
Finite Element ◽  
Free Energy ◽  
Phase Separation ◽  
Space Dimension ◽  
Piecewise Linear ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Linear Finite Element ◽  
Mobility Matrix ◽  
Two Space Dimensions

We consider a model for phase separation of a multi-component alloy with nonsmooth free energy and a concentration dependent mobility matrix. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally numerical experiments with three components in one space dimension are presented.

The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis

1992 ◽  
Vol 3 (2) ◽  
pp. 147-179 ◽  
Author(s):  
J. F. Blowey ◽  
C. M. Elliott
Keyword(s):  
Finite Element ◽  
Free Energy ◽  
Phase Separation ◽  
Variational Inequality ◽  
Numerical Analysis ◽  
Finite Element Approximation ◽  
Gradient Theory ◽  
Element Approximation ◽  
Energy Part ◽  
Two Space Dimensions

In this paper we consider the numerical analysis of a parabolic variational inequality arising from a deep quench limit of a model for phase separation in a binary mixture due to Cahn and Hilliard. Stability, convergence and error bounds for a finite element approximation are proven. Numerical simulations in one and two space dimensions are presented.

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