13 citations · 37 across the 12 of their papers we have counts for
18 papers
Error analysis of a finite element scheme for parametric mean curvature flow based on the DeTurck trick
Klaus Deckelnick, Vanessa Styles
The paper is concerned with the error analysis of a numerical scheme for the approximation of parametric mean curvature flow. The scheme we study is based on a reparametrization us…
Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries
Omar Lakkis, Alexandros Skouras, Vanessa Styles
We study a model for lithium (Li) electrodeposition on Li-metal electrodes that leads to dendritic pattern formation. The model comprises of a system of three coupled PDEs, taking…
Finite element error analysis for a system coupling surface evolution to diffusion on the surface
Klaus Deckelnick, Vanessa Styles
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The…
Finite element approximation of a phase field model for tumour growth
Joe Eyles, Robert Nürnberg, Vanessa Styles
We consider a fully practical finite element approximation of a diffuse interface model for tumour growth that takes the form of a degenerate parabolic system. In addition to showi…
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
We consider a semi-discrete finite element approximation for a system consisting of the evolution of a planar curve evolving by forced curve shortening flow inside a given bounded…
Preconditioning nonlocal multi-phase flow
David Kay, Vanessa Styles
We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen--Cahn variational inequalities. The solver is seen…
A Practical Phase Field Method for an Elliptic Surface PDE
John W. Barrett, Klaus Deckelnick, Vanessa Styles
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadr…
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
We consider a finite element approximation for a system consisting of the evolution of a curve evolving by forced curve shortening flow coupled to a reaction-diffusion equation on…
A tractable mathematical model for tissue growth
Joe Eyles, John F. King, Vanessa Styles
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological…
Hamilton--Jacobi equations on an evolving surface
Klaus Deckelnick, Charles M. Elliott, Tatsu-Hiko Miura +1
We consider the well-posedness and numerical approximation of a Hamilton--Jacobi equation on an evolving hypersurface in . Definitions of viscosity sub- and supersolut…
Cahn--Hilliard inpainting with the double obstacle potential
Harald Garcke, Kei Fong Lam, Vanessa Styles
The inpainting of damaged images has a wide range of applications, and many different mathematical methods have been proposed to solve this problem. Inpainting with the help of Cah…
Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface
Klaus Deckelnick, Vanessa Styles
In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a leve…
Numerical Analysis for a System Coupling Curve Evolution to Reaction-Diffusion on the Curve
John W. Barrett, Klaus Deckelnick, Vanessa Styles
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equatio…
A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws
F. Yang, C. Venkataraman, V. Styles +1
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal con…
A Cahn--Hilliard--Darcy model for tumour growth with chemotaxis and active transport
Harald Garcke, Kei Fong Lam, Emanuel Sitka +1
Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and p…
Whole cell tracking through the optimal control of geometric evolution laws
Konstantinos N. Blazakis, Anotida Madzvamuse, Constantino-Carlos Reyes-Aldasoro +2
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular…
Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient
Klaus Deckelnick, Charles M. Elliott, Vanessa Styles
We propose a double obstacle phase field approach to the recovery of piece-wise constant diffusion coefficients for elliptic partial differential equations. The approach to this in…
Multi-material phase field approach to structural topology optimization
Luise Blank, M. Hassan Farshbaf-Shaker, Harald Garcke +2
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary…