23 citations · 88 across the 22 of their papers we have counts for
29 papers
A filtered time stepping scheme for curve shortening flow for open and closed curves
Klaus Deckelnick, Robert Nürnberg
We propose a filtered time stepping finite element scheme for curve shortening flow of open and closed curves in arbitrary codimension that is second-order accurate in time. Open c…
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…
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…
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 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…
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…