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…