Article

Yang, Fengwei, Venkataraman, Chandrasekhar, Gu, Sai, Styles, Vanessa and Madzvamuse, Anotida (2022) Force estimation during cell migration using mathematical modelling. Journal of Imaging, 8 (7). p. 199. ISSN 2313-433X

Deckelnick, Klaus and Styles, Vanessa (2022) Finite element error analysis for a system coupling surface evolution to diffusion on the surface. Interfaces and Free Boundaries. ISSN 1463-9963

Eyles, Joe, Nurnberg, Robert and Styles, Vanessa (2021) Finite-element approximation of a phase field model for tumour growth. Portugaliae Mathematica, 78 (3/4). pp. 341-365. ISSN 0032-5155

Styles, Vanessa and Van Yperen, James (2021) Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction–diffusion equation on the curve. Numerical Methods for Partial Differential Equations. pp. 1-30. ISSN 0749-159X

Kay, David and Styles, Vanessa (2021) Preconditioning nonlocal multi-phase flow. Journal of Computational Physics, 424. a109715 1-16. ISSN 0021-9991

Barrett, John W, Deckelnick, Klaus and Styles, Vanessa (2020) A practical phase field method for an elliptic surface PDE. IMA Journal of Numerical Analysis. ISSN 0272-4979

Eyles, Joe, King, John R and Styles, Vanessa (2019) A tractable mathematical model for tissue growth. Interfaces and Free Boundaries, 21 (4). pp. 463-493. ISSN 1463-9963

Ryder, Lauren S, Dagdas, Yasin F, Kershaw, Michael J, Venkataraman, Chandrasekhar, Madzvamuse, Anotida, Yan, Xia, Cruz-Mireles, Neftaly, Soanes, Darren M, Oses-Ruiz, Miriam, Styles, Vanessa, Sklenar, Jan, Menke, Frank L H and Talbot, Nicholas J (2019) A sensor kinase controls turgor-driven plant infection by the rice blast fungus. Nature, 574. pp. 423-427. ISSN 0028-0836

Deckelnick, Klaus, Elliott, Charles M, Miura, Tatsu-Hiko and Styles, Vanessa (2019) Hamilton-Jacobi equations on an evolving surface. Mathematics of Computation. ISSN 0025-5718

Garcke, Harald, Lam, Kei Fong and Styles, Vanessa (2018) Cahn--Hilliard inpainting with the double obstacle potential. SIAM Journal on Imaging Sciences, 11 (3). pp. 2064-2089. ISSN 1936-4954

Deckelnick, Klaus and Styles, Vanessa (2018) Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface. Numerische Mathematik, 139 (3). pp. 709-741. ISSN 0029-599X

Barrett, John W, Deckelnick, Klaus and Styles, Vanessa (2017) Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve. SIAM Journal on Numerical Analysis (SINUM), 55 (2). pp. 1080-1100. ISSN 0036-1429

Richardson, G, Please, C and Styles, V (2017) Derivation and solution of effective-medium equations for bulk heterojunction organic solar cells. European Journal of Applied Mathematics, 28 (6). pp. 973-1014. ISSN 0956-7925

Yang, Feng Wei, Venkataraman, Chandrasekhar, Styles, Vanessa and Madzvamuse, Anotida (2017) A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws. Communications in Computational Physics, 21 (1). pp. 65-92. ISSN 1815-2406

Garcke, Harald, Lam, Kei Fong, Sitka, Emanuel and Styles, Vanessa (2016) A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Mathematical Models and Methods in Applied Sciences, 26 (06). pp. 1095-1148. ISSN 0218-2025

Yang, Feng Wei, Venkataraman, Chandrasekhar, Styles, Vanessa, Kuttenberger, V, Horn, E, von Guttenberg, Z and Madzvamuse, Anotida (2016) A computational framework for particle and whole cell tracking applied to a real biological dataset. Journal of Biomechanics, 49 (8). pp. 1290-1304. ISSN 0021-9290

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). a045008. ISSN 0266-5611

Blazakis, Konstantinos N, Madzvamuse, Anotida, Reyes-Aldasoro, Constantino-Carlos, Styles, Vanessa and Venkataraman, Chandrasekhar (2015) Whole cell tracking through the optimal control of geometric evolution laws. Journal of Computational Physics, 297. pp. 495-514. ISSN 0021-9991

Blank, Luise, Garcke, Harald, Farshaf-Shaker, M Hassan and Styles, Vanessa (2014) Relating phase field and sharp interface approaches to structural topology optimization. ESAIM: COCV, 20 (4). pp. 1025-1058. ISSN 1292-8119

Blank, Luise, Garcke, Harald, Sarbu, Lavinia and Styles, Vanessa (2013) Non-local Allen-Cahn systems: analysis and a primal-dual active set method. IMA Journal of Numerical Analysis, 33 (4). pp. 1126-1155. ISSN 0272-4979

Elliott, Charles Martin and Styles, Vanessa (2012) An ALE ESFEM for solving PDEs on evolving surfaces. Milan Journal of Mathematics, 80 (2). pp. 469-501. ISSN 1424-9286

Elliott, Charles M, Stinner, Björn, Styles, Vanessa and Welford, Richard (2011) Numerical computation of advection and diffusion on evolving diffuse interfaces. IMA Journal of Numerical Analysis, 31. pp. 786-812. ISSN 0272-4979

Styles, Vanessa, Elliott, Charles and Deckelnick, Klaus (2011) Numerical analysis of an inverse problem for the eikonal equation. Numerische Mathematik, 119 (2). pp. 245-269. ISSN 0029-599X

Kay, David, Styles, Vanessa and Süli, Endre (2009) Discontinuous Galerkin finite element approximation of the Cahn--Hilliard equation with convection. SIAM Journal on Numerical Analysis, 47 (4). pp. 2660-2685. ISSN 0036-1429

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, 48 (3). pp. 1335-1352. ISSN 0363-0129

Kay, David, Styles, Vanessa and Welford, Richard (2008) Finite element approximation of a Cahn-Hilliard-Navier-Stokes system. Interfaces and Free Boundaries, 10 (1). pp. 15-43. ISSN 1463-9963

Garcke, Harald, Nürnberg, Robert and Styles, Vanessa (2007) Stress and diffusion induced interface motion: Modelling and numerical simulations. European Journal of Applied Mathematics, 18. pp. 631-657. ISSN 0956-7925

Elliott, C M, Kay, D and Styles, V (2005) Finite element analysis of a current density-electric field formulation of Bean's model for superconductivity. IMA Journal of Numerical Analysis, 25 (1). pp. 182-204. ISSN 0272-4979

Garcke, Harald and Styles, Vanessa (2004) Bi-directional diffusion induced grain boundary motion with triple junctions. Interfaces and Free Boundaries, 6 (3). pp. 271-294. ISSN 1463-9971

Barrett, John W, Nürnberg, Robert and Styles, Vanessa (2004) Finite element approximation of a phase field model for void electromigration. SIAM Journal on Numerical Analysis, 42 (2). pp. 738-772. ISSN 0036-1429

Elliott, C M, Kay, D and Styles, V (2004) A finite element approximation of a variational inequality formulation of Bean's model for superconductivity. SIAM Journal on Numerical Analysis, 42 (3). pp. 1324-1341. ISSN 0036-1429

Styles, V and Elliott, C M (2003) Computations of bidirectional grain boundary dynamics in thin metallic films. Journal of Computational Physics, 187 (2). pp. 524-543. ISSN 0021-9991

Styles, V (2002) A note on the convergence in the limit of the long wave mean field superconductivity model to the Bean model. Communications on Pure and Applied Analysis, 1 (4). pp. 485-494. ISSN 1534-0392

Deckelnick, K, Elliott, Charles Martin and Styles, Vanessa (2002) Analysis and computations for a model of quasi-static deformation of a thinning sheet arising in superplastic forming. European Journal of Applied Mathematics, 13 (04). pp. 403-429. ISSN 0956-7925

Styles, Vanessa (2001) Error estimates of a finite-difference approximation for a mean field model of superconducting vortices in one-dimension. IMA Journal of Numerical Analysis, 21 (3). pp. 667-701. ISSN 0272-4979

Elliott, Charles M and Styles, Vanessa (2001) Numerical analysis of a mean field model of superconducting vortices. IMA Journal of Numerical Analysis, 21 (1). pp. 1-51. ISSN 0272-4979

Deckelnick, Klaus, Elliott, Charlie and Styles, Vanessa (2001) Numerical diffusion induced grain boundary motion. Interfaces and Free Boundary, 3 (4). pp. 393-414. ISSN 1463-9963

Elliott, Charles M and Styles, Vanessa (2000) Flux pinning and boundary nucleation of vorticity in a mean field model of superconducting vortices. Interfaces and Free Boundaries, 2. pp. 143-180. ISSN 1463-9963

Schätzle, R and Styles, V (1999) Analysis of a mean field model of superconducting vortices. European Journal of Applied Mathematics, 10 (4). pp. 319-352. ISSN 0956-7925

Book Section

Blazakis, K, Reyes-Aldasoro, C C, Styles, V, Venkataraman, C and Madzvamuse, A (2015) An optimal control approach to cell tracking. In: Louis, Alfred K, Arridge, Simon and Rundell, Bill (eds.) Proceedings of the Inverse Problems from Theory to Applications Conference (IPTA2014). IOP Publishing Ltd, pp. 74-77. ISBN 9780750311069

Conference or Workshop Item

Yang, F, Venkataraman, C, Styles, V and Madzvamuse, A (2015) A parallel and adaptive multigrid solver for the solutions of the optimal control of geometric evolution laws in two and three dimensions. In: 4th International Conference on Computational and Mathematical Biomedical Engineering - CMBE2015, 29 June-1 July 2015, Paris, France.

Elliott, C M and Styles, V M (1999) Numerical approximation of vortex density evolution in a superconductor. In: 18th Dundee Biennial Conference on Numerical Analysis, UNIV DUNDEE, DUNDEE, SCOTLAND, JUN 29-JUL 02, 1999.

Conference Proceedings

Styles, Vanessa and Van Yperen, James (2021) Finite element approximation of a system coupling curve evolution with prescribed normal contact to a fixed boundary to reaction-diffusion on the curve. European Numerical Mathematics and Advanced Applications Conference 2019, The Netherlands, 30th Sept - 4th Oct 2019. Published in: Vermolen, Fred J and Cornelis, Vuik, (eds.) Numerical mathematics and advanced applications ENUMATH 2019. 139 1215-1223. Springer ISSN 1439-7358 ISBN 9783030558734

Elliott, Charles Martin, Stinner, Bjorn, Styles, Vanessa, Venkataraman, Chandrasekhar and Unset (2015) Modelling and simulation of cell migration in heterogeneous media. 4th International Conference Computational & Mathematical Biomedical Engineering, Paris, France, 29 June - 01 July, 2015. Published in: Nithiarasu, Perumal and Budyn, Elisa, (eds.) CMBE15: 4th International Conference on Computational & Mathematical Biomedical Engineering, 29th June - 1st July 2015 École Normale Supéerieure de Cachan, Cachan (Paris) France. 401-404. CMBE, Swansea, UK. ISBN 9780956291431