Barrett, John W., Garcke, Harald and Nürnberg, Robert
(2006)
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid.
Mathematics of Computation (MCOM) 75 (253), pp. 741.
Date of publication of this fulltext: 27 Nov 2009 06:50at publisher (via DOI)
Abstract
We consider a fully practical finite element approximation of the degenerate CahnHilliard equation with elasticity: Find the conserved order parameter, $\theta(x, t)\in [1, 1]$, and the displacement field, $\underline u(x, t)\in \Bbb R^2$, such that $$\gamma\frac{\partial\theta}{\partial t}=\nabla\cdot (b(\theta)\nabla [\gamma\Delta\theta + \gamma^{1}\Psi'(\theta) + \tfrac 12 c' (\theta){\cal ...
Abstract
We consider a fully practical finite element approximation of the degenerate CahnHilliard equation with elasticity: Find the conserved order parameter, , and the displacement field, , such that {}{ t}= (b() [ + ^{1}'() + 12 c' (){ C}{{ E}}( u) : {{ E}}( u)] ), (c(){ C} {{ E}}({u})) = 0, subject to an initial condition on and boundary conditions on both equations. Here is the interfacial parameter, is a nonsmooth double well potential, is the symmetric strain tensor, is the possibly anisotropic elasticity tensor, with and is the degenerate diffusion mobility. In addition to showing stability bounds for our approximation, we prove convergence, and hence existence of a solution to this nonlinear degenerate parabolic system in two space dimensions. Finally, some numerical experiments are presented.
Export bibliographical data
Item type:  Article 

Date:  2006 

Institutions:  Mathematics > Prof. Dr. Harald Garcke 

Identification Number:  Value  Type 

10.1090/S0025571805018028  DOI 


Classification:  Notation  Type 

Primary 65M60, 65M12, 65M50, 35K55, 35K65, 35K35, 82C26, 74F15  MSC 


Keywords:  degenerate CahnHilliard equation; elasticity; convergence; nonlinear degenerate parabolic system 

Dewey Decimal Classification:  500 Science > 510 Mathematics 

Status:  Published 

Refereed:  Unknown 

Created at the University of Regensburg:  Unknown 

Item ID:  10985 
