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Finite element methods for surface PDEs*
In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit
Finite elements on evolving surfaces
In this article, we define a new evolving surface finite-element method for numerically approximating partial differential equations on hypersurfaces (t) in n+1 which evolve with time. The key idea
On the Cahn-Hilliard equation with degenerate mobility
An existence result for the Cahn–Hilliard equation with a concentration dependent diffusional mobility is presented. In particular, the mobility is allowed to vanish when the scaled concentration
Computation of geometric partial differential equations and mean curvature flow
This review concerns the computation of curvature-dependent interface motion governed by geometric partial differential equations. The canonical problem of mean curvature flow is that of finding a
Finite element analysis for a coupled bulk-surface partial differential equation
In this paper, we define a new finite element method for numerically approximating the solution of a partial differential equation in a bulk region coupled with a surface partial differential
On the Cahn-Hilliard equation
where y, Yl and )'2 are constants with y > 0, arises in the study of phase separation in cooling binary solutions such as alloys, glasses and polymer mixtures; see CAHN & HILLIARD [1958],
Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
SummaryA fully discrete finite element method for the Cahn-Hilliard equation with a logarithmic free energy based on the backward Euler method is analysed. Existence and uniqueness of the numerical
The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature
We show by using formal asymptotics that the zero level set of the solution to the Cahn–Hilliard equation with a concentration dependent mobility approximates to lowest order in ɛ. an interface
The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
In this paper we consider the numerical analysis of a parabolic variational inequality arising from a deep quench limit of a model for phase separation in a binary mixture due to Cahn and Hilliard.