188 citations · 1.6k across the 107 of their papers we have counts for
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Willmore Flow of planar networks
Harald Garcke, Julia Menzel, Alessandra Pluda
Geometric gradient flows for elastic energies of Willmore type play an important role in mathematics and in many applications. The evolution of elastic curves has been studied in d…
Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flow with Surfactants
Helmut Abels, Harald Garcke, Josef Weber
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach.…
Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation
John W. Barrett, Harald Garcke, Robert Nürnberg
A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an --gradient flow of an…
A phase field approach to shape optimization in Navier--Stokes flow with integral state constraint
Harald Garcke, Michael Hinze, Christian Kahle +1
We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularizatio…
A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of…
A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities
Luca Dedè, Harald Garcke, Kei Fong Lam
Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to…