Charlie Elliott:-Publications:- Surface PDEs


2013

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 fi nite element method

(G. Dziuk and C. M.Elliott) Math. Comp. 82 (2013) 1--24

2012

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 fi nite elements

(C. M.Elliott, B. Stinner and C. Venkataraman) Journal Royal Society Interface 9(76) (2012) 3027--3044

Computation of two-phase biomembranes with phase dependent material parameters using surface fi nite elements

(C. M. Elliott and B. Stinner) Communications in Computational Physics 13 (2) (2012) 325--360

2011

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

2010

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. Computational Physics 229 (2010) 6585--6612


An h narrow band finite element method for elliptic equations on implicit surfaces

(Klaus Deckelnick, Gerhard Dziuk, Charles M. Elliott and Claus-Justus Heine) IMA Journal Numerical Analysis 30(2010) 351-376


An Eulerian approach to transport and diffusion on evolving implicit surfaces

(G. Dziuk and C. M. Elliott) Computing and Visualization in Science 13 (2010) 17--28

2009

Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface

(C. M. Elliott and B. Stinner) Math. Mod. Meth. Appl. Sci. 19 (2009) 787--802

2008

Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method

(C. Eilks and C. M. Elliott) Jour. Comp. Physics (2008) 227 9727--9741


Eulerian finite element method for parabolic PDES on implicit surfaces

(G. Dziuk and C. M. Elliott) Interfaces and Free Boundaries 10 (2008) 119--138

2007

Surface finite elements for parabolic equations

(G. Dziuk and C. M. Elliott) Journal of Computational Mathematics 25(2007) 385--407


Finite elements on evolving surfaces

(G. Dziuk and C. M. Elliott) IMA Journal Numerical Analysis 27(2007) 262-292


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