SUBMITTED
An abstract framework for parabolic
PDEs on evolving spaces
(Amal Alphonse, Charles M Elliott and Bjorn Stinner)
arXiv preprint arXiv:1403.4500
Error analysis for an ALE evolving
surface finite element method
(C. M. Elliott and C. Venkataraman)
arXiv preprint arXiv:1403.1402
Unfitted finite element methods using bulk
meshes for surface partial differential equations
(Klaus Deckelnick, Charles M Elliott and Thomas Ranner)
arXiv preprint arXiv:1312.2905
Parameter identification problems in the
modelling of cell motility
(Wayne Croft, Charles M Elliott, Graham Ladds,
Bjorn Stinner,
Chandrasekhar Venkataraman and Cathryn Weston)
arXiv preprint arXiv:1311.7602
A multiscale analysis of diffusions
on rapidly varying surfaces
(AB Duncan, CM Elliot, GA Pavliotis and
AM Stuart)
arXiv preprint arXiv:1311.1007
Phase field methods for binary recovery
(C. Brett, A. S. Dedner and C. M. Elliott)
arXiv:1310.4781 (OPTPDE proceedings)
Evolving surface finite element method for the Cahn-Hilliard
equation
(C. M.Elliott and T. Ranner) Numerische Mathematik (to appear)
arxiv:1310.4068
PUBLISHED
Finite element methods for surface PDEs
(G. Dziuk and C. M.Elliott)
Acta Numerica (2013) 289--396
Finite element analysis for a coupled bulk-surface partial
differential equation
(C. M.Elliott and T. Ranner)
IMA Journal Numerical Analysis 33 (2013) 377-402
L2 estimates for the evolving surface finite element method
(G. Dziuk and C. M.Elliott)
Math.
Comp. 82 (2013) 1--24
An ALE ESFEM for solving PDEs on evolving surfaces
(C. M.Elliott and V. M. Styles)
Milan Journal of Mathematics 80 (2012) 469--501
A fully discrete evolving surface finite
element method
(G. Dziuk and C. M.Elliott)
SIAM Journal Numerical Analysis 50 (2012) 2677--2694
Modelling cell motility and chemotaxis with
evolving surface finite elements
(C. M.Elliott, B. Stinner and C. Venkataraman)
Journal Royal Society Interface 9(76) (2012) 3027--3044
(C. M. Elliott and B. Stinner)
Communications in Computational Physics
13 (2) (2012) 325--360
Numerical analysis for an inverse problem for
the eikonal equation
(K. P. Deckelnick, C.M. Elliott and V. Styles)
Numerische Mathematik 119 (2011) 245--269
Surface finite element method for pattern
formation on evolving biological surfaces
(R. Barreira, C. M. Elliott and A. Madzvamuse) J. Math. Biol. 63 (2011) 1095--1119
Numerical computation of advection
and diffusion on evolving diffuse interfaces
(C. M. Elliott, B. Stinner, V. M. Styles and R. Welford) IMAJ Num. Anal. 31 (2011) 245--269
A surface phase field
model for two-phase biological membranes
(C. M. Elliott and B. Stinner) SIAM J. Appl. Math. 70 (2010) 2904--2928
Modelling and computation of two phase geometric biomembranes using surface finite elements
(C. M. Elliott and B. Stinner) J. Comp. Phys. 229 (2010) 6585--6612
An Eulerian approach to transport and diffusion on
evolving surfaces
(G. Dziuk and C.M. Elliott) Computing and Visualization in Science 13 (2010) 17--28
An h-narrow band finite element
method for elliptic equations on implicit surfaces
(K. P. Deckelnick, G. Dziuk, C. M. Elliott and C.-J. Heine) IMAJ Num. Anal. 30 (2010) 351-376