14 papers
A Parametric Finite Element Approach for an Anisotropic Multi-Phase Mullins-Sekerka Problem with Kinetic Undercooling
Tokuhiro Eto, Harald Garcke, Robert Nürnberg
We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolv…
A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface
Harald Garcke, Robert Nürnberg
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving s…
An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting
Harald Garcke, Robert Nürnberg, Quan Zhao
We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of s…
A parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions
Tokuhiro Eto, Harald Garcke, Robert Nürnberg
In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a s…
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…
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…