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Number of items: 53.
2023
Caetano, Diogo, Elliott, Charles M., Grasselli, Maurizio and Poiatti, Andrea (2023) Regularization and separation for evolving surface Cahn-Hilliard equations. SIAM Journal on Mathematical Analysis, 55, (6). pp. 6625-6675. doi:10.1137/22M1497213 ISSN 0036-1410.
Alphonse, Amal, Caetano, Diogo, Djurdjevac, Ana and Elliott, Charles M. (2023) Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs. Journal of Differential Equations, 353 . pp. 268-338. doi:10.1016/j.jde.2022.12.032 ISSN 0022-0396.
2022
Elliott, Charles M., Garcke, Harald and KovΓ‘cs, BalΓ‘zs (2022) Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Numerische Mathematik, 151 . pp. 873-925. doi:10.1007/s00211-022-01301-3 ISSN 0029-599X.
Elliott, Charles M., Hatcher, L. and Stinner, BjΓΆrn (2022) On the sharp interface limit of a phase field model for near-spherical two phase biomembranes. Interfaces and Free Boundaries, 24 (2). pp. 263-286. doi:10.4171/IFB/473 ISSN 1463-9963.
2021
Elliott, Charles M. and Hatcher, L. (2021) Domain formation via phase separation for spherical biomembranes with small deformations. European Journal of Applied Mathematics, 32 (6). pp. 1127-1152. doi:10.1017/S0956792520000297 ISSN 0956-7925.
Caetano, Diogo and Elliott, Charles M. (2021) Cahn-Hilliard equations on an evolving surface. European Journal of Applied Mathematics, 32 (5). pp. 937-1000. doi:10.1017/S0956792521000176 ISSN 0956-7925.
Elliott, Charles M. and Ranner, Thomas (2021) A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains. IMA Journal of Numerical Analysis, 41 (3). pp. 1696-1845. draa062. doi:10.1093/imanum/draa062 ISSN 0272-4979.
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 ISSN 0029-599X.
Elliott, Charles M. and Herbert, P. J. (2020) Second order splitting of a class of fourth order PDEs with point constraints. Mathematics of Computation, 89 . pp. 2613-2648. doi:10.1090/mcom/3556 ISSN 0025-5718.
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 ISSN 1064-8275.
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 ISSN 0266-5611.
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 ISSN 0025-5718.
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 ISSN 0025-5718.
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 ISSN 2166-2525.
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 ISSN 0036-1410.
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 ISSN 0218-2025.
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 ISSN 0272-4979.
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. ISSN 0036-1410.
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 ISSN 0003-9527.
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 ISSN 0362-546X.
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 ISSN 0266-5611.
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 ISSN 2426-8399.
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 ISSN 1364-503X.
Croft, Wayne D., Elliott, Charles M., Ladds, Graham, Stinner, BjΓΆrn, 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 ISSN 0303-6812.
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 ISSN 0036-1410.
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 ISSN 0938-8974.
Alphonse, Amal, Elliott, Charles M. and Stinner, BjΓΆrn (2015) On some linear parabolic PDEs on moving hypersurfaces. Interfaces and Free Boundaries, 17 (2). pp. 157-187. doi:10.4171/IFB/338 ISSN 1463-9963.
Alphonse, Amal, Elliott, Charles M. and Stinner, BjΓΆrn (2015) An abstract framework for parabolic PDEs on evolving spaces. Portugaliae Mathematica, 72 (1). pp. 1-46. doi:10.4171/PM/1955 ISSN 0032-5155.
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 ISSN 0036-1429.
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 ISSN 1439-7358.
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 ISSN 0962-4929.
Elliott, Charles M. and Stinner, BjΓΆrn (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 ISSN 1815-2406.
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 ISSN 0272-4979.
2012
Elliott, Charles M., Stinner, BjΓΆrn 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 ISSN 1742-5689.
Stinner, BjΓΆrn, 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) LΒ² -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 ISSN 0025-5718.
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 ISSN 1424-9286.
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 ISSN 1095-7170.
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 ISSN 0303-6812.
Elliott, Charles M., Stinner, BjΓΆrn, 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 ISSN 0272-4979.
Elliott, Charles M. and Stinner, BjΓΆrn (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 ISSN 0029-599X.
2010
Elliott, Charles M. and Stinner, BjΓΆrn (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 ISSN 0021-9991.
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 ISSN 0272-4979.
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 ISSN 1432-9360.
Elliott, Charles M. and Stinner, BjΓΆrn (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 ISSN 0036-1399.
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 ISSN 0272-4979.
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, BjΓΆrn (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 ISSN 0218-2025.
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 ISSN 0363-0129.
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 ISSN 0021-9991.
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 ISSN 1463-9963.
Stinner, BjΓΆrn, Elliott, Charles M., Garcke, Harald, Niethammer, Barbara, Peletier, Mark and RΓΆger, 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 ISSN 1660-8933.
This list was generated on Thu Mar 28 09:50:47 2024 GMT.