188 citations · 1.6k across the 107 of their papers we have counts for
116 papers
A unified energy-stable finite element approximation for evolving fluidic biomembranes
Harald Garcke, Robert Nürnberg, Quan Zhao
We present a unified finite element method for the dynamics of fluidic biomembranes. The model is governed by the Navier--Stokes equations in the bulk coupled to the surface Navier…
On a Mullins-Sekerka model for the growth of active droplets modelling protocells: Stability analysis and numerical computations
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
Mullins-Sekerka models with chemical reactions can lead to scenarios where droplets grow, become unstable, split, grow and undergo further division. These grow and division cycles…
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…