2021

Caetano, Diogo and Elliott, Charles M. (2021) Cahn-Hilliard equations on an evolving surface. European Journal of Applied Mathematics . doi:10.1017/S0956792521000176 (In Press)

2020

Church, Lewis, Djurdjevac, Ana and Elliott, Charles M. (2020) A domain mapping approach for elliptic equations posed on random bulk and surface domains. Numerische Mathematik, 146 . pp. 1-49. doi:10.1007/s00211-020-01139-7

Elliott, Charles M. and Hatcher, L. (2020) Domain formation via phase separation for spherical biomembranes with small deformations. European Journal of Applied Mathematics . doi:10.1017/S0956792520000297 (In Press)

Dunbar, Oliver R. A., Dunlop, Matthew M., Elliott, Charles M., Hoang, Viet Ha and Stuart, Andrew M. (2020) Reconciling Bayesian and perimeter regularization for binary inversion. SIAM Journal on Scientific Computing, 42 (4). A1984-A2013. doi:10.1137/18M1179559

Elliott, Charles M. and Herbert, P. J. (2020) Second order splitting of a class of fourth order PDEs with point constraints. Mathematics of Computation . (In Press)

Elliott, Charles M. and Ranner, Thomas (2020) A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains. IMA Journal of Numerical Analysis . draa062. doi:10.1093/imanum/draa062

2019

Dunbar, Oliver and Elliott, Charles M. (2019) Binary recovery via phase field regularization for first-arrival traveltime tomography. Inverse Problems, 35 (9). 095004. doi:10.1088/1361-6420/ab1c6c

Elliott, Charles M., Fritz, Hans and Hobbs, Graham (2019) Second order splitting for a class of fourth order equations. Mathematics of Computation, 88 . pp. 2605-2634. doi:10.1090/mcom/3425

Deckelnick, Klaus, Elliott, Charles M., Miura, Tatsu-Hiko and Styles, Vanessa (2019) Hamilton-Jacobi equations on an evolving surface. Mathematics of Computation, 88 . pp. 2635-2664. doi:10.1090/mcom/3420

2018

Djurdjevac, Ana, Elliott, Charles M., Kornhuber, Ralf and Ranner, Thomas (2018) Evolving surface finite element methods for random advection-diffusion equations. SIAM/ASA Journal on Uncertainty Quantification, 6 (4). pp. 1656-1684. doi:10.1137/17M1149547

Alphonse, Amal, Elliott, Charles M. and Terra, Joana (2018) A coupled ligand-receptor bulk-surface system on a moving domain : well posedness, regularity and convergence to equilibrium. SIAM Journal on Mathematical Analysis, 50 (2). pp. 1544-1592. doi:10.1137/16M110808X

2017

Elliott, Charles M., Fritz, Hans and Hobbs, Graham (2017) Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Mathematical Models and Methods in Applied Sciences, 27 (8). pp. 1547-1586. doi:10.1142/s0218202517500269

Elliott, Charles M. and Fritz, Hans (2017) On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick. IMA Journal of Numerical Analysis, 37 (2). pp. 543-603. doi:10.1093/imanum/drw020

Elliott, Charles M., Ranner, Thomas and Venkataraman, Chandrasekhar (2017) Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, 49 (1). pp. 360-397.

2016

Elliott, Charles M., Graser, Carsten, Hobbs, Graham, Kornhuber, R. and Wolf, Maren-Wanda (2016) A variational approach to particles in lipid membranes. Archive for Rational Mechanics and Analysis, 222 (2). pp. 1011-1075. doi:10.1007/s00205-016-1016-9

Alphonse, Amal and Elliott, Charles M. (2016) Well-posedness of a fractional porous medium equation on an evolving surface. Nonlinear Analysis: Theory, Methods & Applications, 137 . pp. 3-42. doi:10.1016/j.na.2016.01.010

Deckelnick, Klaus, Elliott, Charles M. and Styles, Vanessa (2016) Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient. Inverse Problems, 32 (4). 045008. doi:10.1088/0266-5611/32/4/045008

Elliott, Charles M. and Fritz, Hans (2016) On algorithms with good mesh properties for problems with moving boundaries based on the harmonic map heat flow and the DeTurck trick. Journal of Computational Mathematics, 2 . pp. 141-176. doi:10.5802/smai-jcm.12

2015

Alphonse, Amal and Elliott, Charles M. (2015) A Stefan problem on an evolving surface. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373 (2050). doi:10.1098/rsta.2014.0279

Croft, Wayne D., Elliott, Charles M., Ladds, Graham, Stinner, Björn, Venkataraman, Chandrasekhar and Weston, Cathryn (2015) Parameter identification problems in the modelling of cell motility. Journal of Mathematical Biology, 71 (2). pp. 399-436. doi:10.1007/s00285-014-0823-6

Elliott, Charles M. and Fritz, Hans (2015) Time-periodic solutions of advection-diffusion equations on moving hypersurfaces. SIAM Journal on Mathematical Analysis, 47 (3). pp. 1693-1718. doi:10.1137/140977060

Duncan, A. B., Elliott, Charles M., Pavliotis, G. A. and Stuart, A. M. (2015) A multiscale analysis of diffusions on rapidly varying surfaces. Journal of Nonlinear Science, 25 (2). pp. 389-449. doi:10.1007/s00332-015-9237-x

Alphonse, Amal, Elliott, Charles M. and Stinner, Björn (2015) On some linear parabolic PDEs on moving hypersurfaces. Interfaces and Free Boundaries, 17 (2). pp. 157-187. doi:10.4171/IFB/338

Alphonse, Amal, Elliott, Charles M. and Stinner, Björn (2015) An abstract framework for parabolic PDEs on evolving spaces. Portugaliae Mathematica, 72 (1). pp. 1-46. doi:10.4171/PM/1955

2014

Deckelnick, Klaus, Elliott, Charles M. and Ranner, Thomas (2014) Unfitted finite element methods using bulk meshes for surface partial differential equations. SIAM Journal on Numerical Analysis, Volume 52 (Number 4). pp. 2137-2162. doi:10.1137/130948641

Brett, Charles E. A., Elliott, Charles M. and Dedner, Andreas (2014) Phase field methods for binary recovery. Optimization with PDE Constraints, 101 . pp. 25-63. doi:10.1007/978-3-319-08025-3_2

2013

Dziuk, Gerhard and Elliott, Charles M. (2013) Finite element methods for surface PDEs. Acta Numerica, Volume 22 . pp. 289-396. doi:10.1017/S0962492913000056

Elliott, Charles M. and Stinner, Björn (2013) Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Communications in Computational Physics, Vol.13 (No.2). pp. 325-360. doi:10.4208/cicp.170611.130112a

Elliott, Charles M. and Ranner, T. (2013) Finite element analysis for a coupled bulk-surface partial differential equation. IMA Journal of Numerical Analysis, Volume 33 (Number 2). pp. 377-402. doi:10.1093/imanum/drs022

2012

Elliott, Charles M., Stinner, Björn and Venkataraman, Chandrasekhar (2012) Modelling cell motility and chemotaxis with evolving surface finite elements. Journal of The Royal Society Interface, Volume 9 (Number 76). pp. 3027-3044. doi:10.1098/rsif.2012.0276

Stinner, Björn, Venkataraman, Chandrasekhar and Elliott, Charles M. (2012) Application of elastic flows to cell motility. In: International Conference on Free Boundary Problems : Theory and Applications, Chiemsee, Germany, 11-15 Jun 2012 (Unpublished)

Dziuk, Gerhard and Elliott, Charles M. (2012) L² -estimates for the evolving surface finite element method. Mathematics of Computation, Volume 82 (Number 281). pp. 1-24. doi:10.1090/S0025-5718-2012-02601-9

Elliott, Charles M. and Styles, Vanessa (2012) An ALE ESFEM for solving PDEs on evolving surfaces. Milan Journal of Mathematics, Volume 80 (Number 2). pp. 469-501. doi:10.1007/s00032-012-0195-6

Dziuk, Gerhard and Elliott, Charles M. (2012) A fully discrete evolving surface finite element method. SIAM Journal of Numerical Analysis, Vol.50 (No.5). pp. 2677-2694. doi:10.1137/110828642

2011

Barreira, R., Elliott, Charles M. and Madzvamuse, A. (2011) The surface finite element method for pattern formation on evolving biological surfaces. Journal of Mathematical Biology, Vol.63 (No.6). pp. 1095-1119. doi:10.1007/s00285-011-0401-0

Elliott, Charles M., Stinner, Björn, Styles, Vanessa and Welford, R. (2011) Numerical computation of advection and diffusion on evolving diffuse interfaces. IMA Journal of Numerical Analysis, Vol.31 (No.3). pp. 786-812. doi:10.1093/imanum/drq005

Elliott, Charles M. and Stinner, Björn (2011) PDEs on diffuse interfaces with applications to two-phase flow. In: Workshop on Phase Field Models in Fluid Mechanics, Regensburg, Germany, 14-16 Feb 2011 (Unpublished)

Deckelnick, Klaus, Elliott, Charles M. and Styles, Vanessa (2011) Numerical analysis of an inverse problem for the eikonal equation. Numerische Mathematik, Volume 119 (Number 2). pp. 245-269. doi:10.1007/s00211-011-0386-z

2010

Elliott, Charles M. and Stinner, Björn (2010) Modeling and computation of two phase geometric biomembranes using surface finite elements. Journal of Computational Physics, Vol.229 (No.18). pp. 6585-6612. doi:10.1016/j.jcp.2010.05.014

Deckelnick, Klaus, Dziuk, Gerhard, Elliott, Charles M. and Heine, Claus-Justus (2010) An h-narrow band finite-element method for elliptic equations on implicit surfaces. IMA Journal of Numerical Analysis, Vol.30 (No.2). pp. 351-376. doi:10.1093/imanum/drn049

Dziuk, Gerhard and Elliott, Charles M. (2010) An Eulerian approach to transport and diffusion on evolving implicit surfaces. Computing and Visualization in Science, Vol.13 (No.1). pp. 17-28. doi:10.1007/s00791-008-0122-0

Elliott, Charles M. and Stinner, Björn (2010) A surface phase field model for two-phase biological membranes. SIAM Journal on Applied Mathematics, Volume 70 (Number 8). pp. 2904-2928. doi:10.1137/090779917

2009

Elliott, Charles M. and Smitheman, S. A. (2009) Numerical analysis of the TV regularization and H-1 fidelity model for decomposing an image into cartoon plus texture. IMA Journal of Numerical Analysis, Vol.29 (No.3). pp. 651-689. doi:10.1093/imanum/drn025

Elliott, Charles M. (2009) Computational surface partial differential equations. In: ENUMATH 2009, Uppsala, Sweden, 29 Jun-03 Jul 2009 (Unpublished)

Elliott, Charles M. and Stinner, Björn (2009) Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Mathematical Models and Methods in Applied Sciences, Vol.19 (No.5). pp. 787-802. doi:10.1142/S0218202509003620

Deckelnick, Klaus, Elliott, Charles M. and Styles, Vanessa (2009) Optimal control of the propagation of a graph in inhomogeneous media. SIAM Journal on Control and Optimization, Vol.48 (No.3). pp. 1335-1352. doi:10.1137/080723648

2008

Eilks, C. and Elliott, Charles M. (2008) Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Journal of Computational Physics, Vol.227 (No.23). pp. 9727-9741. doi:10.1016/j.jcp.2008.07.023

Dziuk, Gerhard and Elliott, Charles M. (2008) Eulerian finite element method for parabolic PDEs on implicit surfaces. Interfaces and Free Boundaries, Volume 10 (Number 1). pp. 119-138. doi:10.4171/IFB/182

Stinner, Björn, Elliott, Charles M., Garcke, Harald, Niethammer, Barbara, Peletier, Mark and Röger, Matthias (2008) Lateral phase separation on biomembranes. In: Mini-Workshop: Mathematics of Biological Membranes. Oberwolfach Reports, Vol.5 (No.3). pp. 2293-2336. doi:10.4171/OWR/2008/41