404 citations · 3.5k across the 79 of their papers we have counts for
82 papers
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…
A finite element error analysis for axisymmetric mean curvature flow
John W. Barrett, Klaus Deckelnick, Robert Nürnberg
We consider the numerical approximation of axisymmetric mean curvature flow with the help of linear finite elements. In the case of a closed genus-1 surface, we derive optimal erro…
Stable approximations for axisymmetric Willmore flow for closed and open surfaces
John W. Barrett, Harald Garcke, Robert Nürnberg
For a hypersurface in , Willmore flow is defined as the --gradient flow of the classical Willmore energy: the integral of the squared mean curvature. This geome…
Finite spectral triples for the fuzzy torus
John W. Barrett, James Gaunt
Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli de…
Parametric finite element approximations of curvature driven interface evolutions
John W. Barrett, Harald Garcke, Robert Nürnberg
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution eq…
Spectral estimators for finite non-commutative geometries
John W. Barrett, Paul Druce, Lisa Glaser
A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how…