188 citations · 1.6k across the 107 of their papers we have counts for
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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…
Stable fully practical finite element methods for axisymmetric Willmore flow
Harald Garcke, Robert Nürnberg, Quan Zhao
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to…
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…
An energy-stable minimal deformation rate scheme for mean curvature flow and surface diffusion
Guangwei Gao, Harald Garcke, Buyang Li +1
We propose a new parametric finite element method, referred to as the BGN-MDR method, for simulating both mean curvature flow and surface diffusion for closed hypersurfaces, as wel…
On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not g…