6 papers
On the basin of attraction for the free boundary free elastic flow
Klaus Deckelnick, Hans-Christoph Grunau, Robert Nürnberg +2
The free boundary free elastic flow is the steepest descent gradient flow for the elastic energy of curves meeting parallel lines perpendicularly. In this article we prove that the…
Second order in time finite element schemes for curve shortening flow and curve diffusion
Klaus Deckelnick, Robert Nürnberg
We prove optimal error bounds for a second order in time finite element approximation of curve shortening flow in possibly higher codimension. In addition, we introduce a second or…
Finite element schemes with tangential motion for fourth order geometric curve evolutions in arbitrary codimension
Klaus Deckelnick, Robert Nürnberg
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a spe…
Quasi-optimal error estimate for the approximation of the elastic flow of inextensible curves
Sören Bartels, Klaus Deckelnick, Dominik Schneider
A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable disc…
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…
Finite element approximation to the non-stationary quasi-geostrophic equation
Dohyun Kim, Amiya K. Pani, Eun-Jae Park
In this paper, C1-conforming element methods are analyzed for the stream function formulation of a single layer non-stationary quasi-geostrophic equation in the ocean circulation m…