2 citations · 3 across the 4 of their papers we have counts for
6 papers
Second order splitting for a class of fourth order equations
Charles M. Elliott, Hans Fritz, Graham Hobbs
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems. In this way we develop an approach to a class of fourth order elliptic part…
On the computation of harmonic maps by unconstrained algorithms based on totally geodesic embeddings
Hans Fritz
In this paper, we present an algorithm for the computation of harmonic maps, and respectively, of the harmonic map heat flow between two closed Riemannian manifolds. Our approach i…
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes
Charles M. Elliott, Hans Fritz, Graham Hobbs
In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is sui…
On algorithms with good mesh properties for problems with moving boundaries based on the Harmonic Map Heat Flow and the DeTurck trick
Charles M. Elliott, Hans Fritz
In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with bound…
On Approximations of the Curve Shortening Flow and of the Mean Curvature Flow based on the DeTurck trick
Charles M. Elliott, Hans Fritz
In this paper we discuss novel numerical schemes for the computation of the curve shortening and mean curvature flows that are based on special reparametrizations. The main idea is…
Time-periodic solutions of advection-diffusion equations on moving hypersurfaces
Charles M. Elliott, Hans Fritz
In this paper we study time-periodic solutions to advection-diffusion equations of a scalar quantity on a periodically moving -dimensional hypersurface $Γ(t) \subset \mathbb…