An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix

2001 ◽  
Vol 88 (2) ◽  
pp. 255-297 ◽  
Author(s):  
John W. Barrett ◽  
James F. Blowey
Keyword(s):  
Finite Element ◽  
Phase Separation ◽  
Error Bound ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Mobility Matrix

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.

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