Finite Element Approximation of a Phase Field Model for Void Electromigration. - John W. Barrett 001; Robert Nürnberg; Vanessa Styles (SIAM J. Numer. Anal., 2004)

A Finite Element Approximation of a Variational Inequality Formulation of Bean's Model for Superconductivity. - Charles M. Elliott; David Kay; Vanessa Styles (SIAM J. Numer. Anal., 2004)

Optimal Control of the Propagation of a Graph in Inhomogeneous Media. - Klaus Deckelnick; Charles M. Elliott; Vanessa Styles (SIAM J. Control. Optim., 2009)

Discontinuous Galerkin Finite Element Approximation of the Cahn-Hilliard Equation with Convection. - David Kay; Vanessa Styles; Endre Süli (SIAM J. Numer. Anal., 2009)

Numerical analysis of an inverse problem for the eikonal equation. - Klaus Deckelnick; Charles M. Elliott; Vanessa Styles (Numerische Mathematik, 2011)

Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques. - Luise Blank; Martin Butz; Harald Garcke; Lavinia Sarbu; Vanessa Styles (Constrained Optimization and Optimal Control for Partial Differential Equations, 2012)

Phase-field Approaches to Structural Topology Optimization. - Luise Blank; Harald Garcke; Lavinia Sarbu; Tarin Srisupattarawanit; Vanessa Styles; Axel Voigt (Constrained Optimization and Optimal Control for Partial Differential Equations, 2012)

Whole cell tracking through the optimal control of geometric evolution laws. - Konstantinos N. Blazakis; Anotida Madzvamuse; Constantino Carlos Reyes-Aldasoro; Vanessa Styles; Chandrasekhar Venkataraman (J. Comput. Phys., 2015)

Numerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the Curve. - John W. Barrett 001; Klaus Deckelnick; Vanessa Styles (SIAM J. Numer. Anal., 2017)

Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface. - Klaus Deckelnick; Vanessa Styles (Numerische Mathematik, 2018)

Cahn-Hilliard Inpainting with the Double Obstacle Potential. - Harald Garcke; Kei Fong Lam; Vanessa Styles (SIAM J. Imaging Sci., 2018)

Finite Element Approximation of a System Coupling Curve Evolution with Prescribed Normal Contact to a Fixed Boundary to Reaction-Diffusion on the Curve. - Vanessa Styles; James Van Yperen (ENUMATH, 2019)

Hamilton-Jacobi equations on an evolving surface. - Klaus Deckelnick; Charles M. Elliott; Tatsu-Hiko Miura; Vanessa Styles (Math. Comput., 2019)

A Practical Phase Field Method for an Elliptic Surface PDE. - John W. Barrett 001; Klaus Deckelnick; Vanessa Styles (CoRR, 2020)

Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction-diffusion equation on the curve. - Vanessa Styles; James Van Yperen (CoRR, 2020)

Finite element approximation of a phase field model for tumour growth. - Joe Eyles; Robert Nürnberg; Vanessa Styles (CoRR, 2020)

Finite element error analysis for a system coupling surface evolution to diffusion on the surface. - Klaus Deckelnick; Vanessa Styles (CoRR, 2021)

Preconditioning nonlocal multi-phase flow. - David Kay; Vanessa Styles (J. Comput. Phys., 2021)

Force Estimation during Cell Migration Using Mathematical Modelling. - Fengwei Yang; Chandrasekhar Venkataraman; Sai Gu; Vanessa Styles; Anotida Madzvamuse (J. Imaging, 2022)

Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries. - Omar Lakkis; Alexandros Skouras; Vanessa Styles (CoRR, 2023)