5 papers · 1 filter
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…
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…