PDEs on surfaces


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) 786--812

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


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


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


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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