Mathematics of Computation
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
A multigrid finite element solver for the Cahn-Hilliard equation
Journal of Computational Physics
A discontinuous Galerkin method for the Cahn-Hilliard equation
Journal of Computational Physics
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
Journal of Computational Physics
Journal of Computational Physics
Finite Element Approximation of a Three Dimensional Phase Field Model for Void Electromigration
Journal of Scientific Computing
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations
Journal of Computational Physics
A conservative numerical method for the Cahn-Hilliard equation in complex domains
Journal of Computational Physics
On linear schemes for a Cahn-Hilliard diffuse interface model
Journal of Computational Physics
Journal of Computational Physics
Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Efficient Solvers of Discontinuous Galerkin Discretization for the Cahn---Hilliard Equations
Journal of Scientific Computing
Journal of Computational Physics
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We consider a fully practical finite element approximation of the Cahn--Hilliard equation with degenerate mobility $$ \textstyle \frac{\partial u}{\partial t}= \del .(\,b(u)\, \del (-\gamma\lap u+\Psi'(u))) , $$ where $b(\cdot)\geq 0$ is a diffusional mobility and $\Psi(\cdot)$ is a homogeneous free energy. In addition to showing well posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore, an iterative scheme for solving the resulting nonlinear discrete system is analyzed. We also discuss how our approximation has to be modified in order to be applicable to a logarithmic homogeneous free energy. Finally, some numerical experiments are presented.