Zobrazeno 1 - 10
of 2 789
pro vyhledávání: '"ELLIOTT, P. M."'
We consider the surface Stokes equation with Lagrange multiplier and approach it numerically. Using a Taylor-Hood surface finite element method, along with an appropriate estimation for the additional Lagrange multiplier, we establish optimal converg
Externí odkaz:
http://arxiv.org/abs/2410.19470
We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane curvature
Externí odkaz:
http://arxiv.org/abs/2410.05492
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type problems on an
Externí odkaz:
http://arxiv.org/abs/2407.16522
Autor:
Elliott, Charles M., Sales, Thomas
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 particular we establish optimal order error bounds for a (fully implicit) b
Externí odkaz:
http://arxiv.org/abs/2405.11984
Autor:
Elliott, Charles M., Sales, Thomas
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-posedness for the corresponding (tangential) system when one prescribes th
Externí odkaz:
http://arxiv.org/abs/2401.12044
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions. This is ac
Externí odkaz:
http://arxiv.org/abs/2212.13288
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3, 2021, doi:10.1
Externí odkaz:
http://arxiv.org/abs/2208.04850
We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in $\mathbb R^3$, as well as a related weighted model. The well-posedness of weak solutions for the correspo
Externí odkaz:
http://arxiv.org/abs/2205.09822
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface, inspired by a
Externí odkaz:
http://arxiv.org/abs/2202.03302
We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of known nodes at an initial time, to all other unknown nodes at later times with
Externí odkaz:
http://arxiv.org/abs/2201.07577