Dziuk's surface finite element method (FEM) for mean curvature flow has had a significant
impact on the development of parametric and evolving surface FEMs for surface evolution …

An evolving surface finite element discretisation is analysed for the evolution of a closed two-
dimensional surface governed by a system coupling a generalised forced mean curvature …

Aiming at simulating elastic rods, we discretize a rod model based on a general theory of
hyperelasticity for inextensible and unshearable rods. After reviewing this model and …

We propose and analyze a semidiscrete parametric finite element scheme for solving the
area-preserving curve shortening flow. The scheme is based on Dziuk's approach [SIAM J …

We develop a unified theory for continuous-in-time finite element discretizations of partial
differential equations posed in evolving domains, including the consideration of equations …

For a parabolic surface partial differential equation coupled to surface evolution,
convergence of the spatial semidiscretization is studied in this paper. The velocity of the …

We consider a finite element approximation for a system consisting of the evolution of a
closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation …

The evolution of a closed two-dimensional surface driven by both mean curvature flow and a
reaction–diffusion process on the surface is formulated as a system that couples the velocity …

We prove a short time existence result for a system consisting of a geometric evolution
equation for a hypersurface and a parabolic equation on this evolving hypersurface. More …

We consider a system consisting of a geometric evolution equation for a hypersurface and a
parabolic equation on this evolving hypersurface. More precisely, we discuss mean …