4 papers
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…
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…