Journal ArticleDOI
An error bound for the finite element approximation of a model for phase separation of a multi-component alloy
John W. Barrett,James F. Blowey +1 more
TLDR
In this paper, an error bound is proved for a piecewise linear finite element approximation, using a backward-Euler time discretization, of a model for phase separation of a multi-component alloy.Abstract:
An error bound is proved for a fully practical piecewise linear finite element approximation, using a backward-Euler time discretization, of a model for phase separation of a multi-component alloy. Numerical experiments with three components in one and two space dimensions are also presented.read more
Citations
More filters
Journal ArticleDOI
Phase field modeling and simulation of three-phase flows
Junseok Kim,John Lowengrub +1 more
TL;DR: A stable conservative, second order accurate fully implicit fully implicit discre tization of the NS and three-phase (ternary) CH system and uses a nonlinear multigrid method to efficiently solve the dis crete ternary CH system at the implicit time-level.
Journal ArticleDOI
Error analysis of a mixed finite element method for the Cahn-Hilliard equation
Xiaobing Feng,Andreas Prohl +1 more
TL;DR: It is shown that all error bounds depend on only in some lower polynomial order for small ɛ, and convergence of the fully discrete finite element solution to the solution of the Hele-Shaw (Mullins-Sekerka) problem is proved.
Journal ArticleDOI
Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility
John W. Barrett,James F. Blowey +1 more
TL;DR: It is proved that there exists a unique solution for sufficiently smooth initial data in the Cahn-Hilliard equation and an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions is proved.
Journal ArticleDOI
Numerical schemes for a three component Cahn-Hilliard model
Franck Boyer,Sebastian Minjeaud +1 more
TL;DR: In this paper, the authors investigated numerical schemes for solving a three component Cahn-Hilliard model, where the space discretization is performed by using a Galerkin formulation and the finite element method.
Journal ArticleDOI
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential
TL;DR: The unique solvability and the positivity-preserving property for the second order scheme are proved using similar ideas, in which the singular nature of the logarithmic term plays an essential role.
References
More filters
Journal ArticleDOI
Splitting Algorithms for the Sum of Two Nonlinear Operators
P. L. Lions,B. Mercier +1 more
TL;DR: This work studies two splitting algorithms for (stationary and evolution) problems involving the sum of two monotone operators with real-time requirements.
Journal ArticleDOI
The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
TL;DR: In this article, a mathematical analysis is carried out for the Cahn-Hilliard equation where the free energy takes the form of a double well potential function with infinite walls, and the existence and uniqueness are proved for a weak formulation of the problem which possesses a Lyapunov functional.
Journal ArticleDOI
Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
TL;DR: In this paper, a fully discrete finite element method for the Cahn-Hilliard equation with a logarithmic free energy based on the backward Euler method is analyzed and the existence and uniqueness of the numerical solution and its convergence to the solution of the continuous problem are proved.
Journal ArticleDOI
Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation
Charles M. Elliott,Stig Larsson +1 more
TL;DR: In this article, a finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidiscrete case and in a completely discrete case based on the backward Euler method.