8 citations · 14 across the 7 of their papers we have counts for
7 papers
Small deformations of a near cylindrical tube for the Canham-Helfrich Energy with applications to biological membranes
Charles M. Elliott, Carsten Gräser, Philip J. Herbert
In this article we develop a quadratic energy which approximates the Canham-Helfrich energy for a tube-like surface with clamped boundary and area constraint. The energy is suited…
An iterative approach to a fluid-rigid body interaction problem
Charles M. Elliott, Thomas Sales
We study a novel approach for the existence of solutions to an incompressible fluid-rigid body interaction problem in three dimensions. Our approach introduces an iteration based o…
An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential
Charles M. Elliott, Thomas Sales
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we conside…
The evolving surface Cahn-Hilliard equation with a degenerate mobility
Charles M. Elliott, Thomas Sales
We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-stro…
A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential
Charles M. Elliott, Thomas Sales
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In parti…
Navier-Stokes-Cahn-Hilliard equations on evolving surfaces
Charles M. Elliott, Thomas Sales
We derive a system of equations which can be seen as an evolving surface version of the diffuse interface "Model H" of Hohenberg and Halperin (1977). We then consider the well-pose…
Error analysis for an ALE evolving surface finite element method
Charles M. Elliott, Chandrasekhar Venkataraman
We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a m…