C. Elliott

Publications184
h-index50
Citations9,324
Highly Influential Citations586
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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…
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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…
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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…
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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…
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Weak and variational methods for moving boundary problems
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…
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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],…
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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…
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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…
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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.…
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