A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation
SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Numerical analysis of a continuum model of phase transition
SIAM Journal on Numerical Analysis
On the Cahn-Hilliard equation with degenerate mobility
SIAM Journal on Mathematical Analysis
Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
C0 Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains
Journal of Scientific Computing
A finite element method for surface diffusion: the parametric case
Journal of Computational Physics
Multigrid Algorithms for C0 Interior Penalty Methods
SIAM Journal on Numerical Analysis
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
Journal of Computational Physics
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations
Journal of Computational Physics
A nonconforming finite element method for the Cahn-Hilliard equation
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
A conservative numerical method for the Cahn-Hilliard equation in complex domains
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
A quantitative comparison between C0 and C1 elements for solving the Cahn-Hilliard equation
Journal of Computational Physics
Journal of Computational Physics
High accuracy solutions to energy gradient flows from material science models
Journal of Computational Physics
Efficient Solvers of Discontinuous Galerkin Discretization for the Cahn---Hilliard Equations
Journal of Scientific Computing
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A discontinuous Galerkin finite element method has been developed to treat the high-order spatial derivatives appearing in the Cahn-Hilliard equation. The Cahn-Hilliard equation is a fourth-order nonlinear parabolic partial differential equation, originally proposed to model phase segregation of binary alloys. The developed discontinuous Galerkin approach avoids the need for mixed finite element methods, coupled equations or interpolation functions with a high degree of continuity that have been employed in the literature to treat the fourth-order spatial derivatives. The variational formulation of the discontinuous Galerkin method, its implementation and numerical examples are presented. In this communication, it is also shown under what conditions the method is stable, and an error estimate in an energy-type norm is presented. The method is evaluated by comparison with a standard finite element treatment in which the Cahn-Hilliard equation is decomposed into two coupled partial differential equations.