70 citations · 244 across the 29 of their papers we have counts for
5 papers · 1 filter
A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity and convergence to equilibrium
Amal Alphonse, Charles M. Elliott, Joana Terra
We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The…
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes
Charles M. Elliott, Hans Fritz, Graham Hobbs
In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is sui…
On algorithms with good mesh properties for problems with moving boundaries based on the Harmonic Map Heat Flow and the DeTurck trick
Charles M. Elliott, Hans Fritz
In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with bound…
Solving reaction-diffusion equations on evolving surfaces defined by biological image data
Till Bretschneider, Cheng-Jin Du, Charles M. Elliott +2
We present a computational approach for solving reaction-diffusion equations on evolving surfaces which have been obtained from cell image data. It is based on finite element space…
On Approximations of the Curve Shortening Flow and of the Mean Curvature Flow based on the DeTurck trick
Charles M. Elliott, Hans Fritz
In this paper we discuss novel numerical schemes for the computation of the curve shortening and mean curvature flows that are based on special reparametrizations. The main idea is…