93 citations · 105 across the 6 of their papers we have counts for
6 papers
Stable fully discrete finite element methods with BGN tangential motion for Willmore flow of planar curves
Harald Garcke, Robert Nürnberg, Quan Zhao
We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolut…
Isoparametric finite element methods for mean curvature flow and surface diffusion
Harald Garcke, Robert Nürnberg, Simon Praetorius +1
We propose higher-order isoparametric finite element approximations for mean curvature flow and surface diffusion. The methods are natural extensions of the piecewise linear finite…
On the numerical approximation of hyperbolic mean curvature flows for surfaces
Klaus Deckelnick, Robert Nürnberg
The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in . For each evolution law we propose both a finite elem…
Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces
Klaus Deckelnick, Robert Nürnberg
We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the…
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…
Stable discretizations of elastic flow in Riemannian manifolds
John W. Barrett, Harald Garcke, Robert Nürnberg
The elastic flow, which is the -gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elas…