13 papers
On a visco-elastic Mullins-Sekerka System
Helmut Abels, Harald Garcke, Jonas Haselböck
We introduce a novel visco-elastic Mullins-Sekerka system with a prescribed constant contact angle at the boundary. The system is derived as an --type gradient flow of…
A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity
Harald Garcke, Jiashun Hu, Nuo Lei
We propose a gravity-consistent arbitrary Lagrangian--Eulerian finite element method for incompressible Navier--Stokes free-boundary problems with moving contact lines. A direct bo…
Local Well-Posedness for a Diffuse Interface Model for Two-Phase Flows from Mixture Theory
Helmut Abels, Harald Garcke, Julia Wittmann
Local-in-time well-posedness is established for a recently proposed diffuse interface model describing incompressible two-phase flows. The result constitutes the first analytical s…
Weak and strong solutions for a class of quasilinear Allen--Cahn systems
Harald Garcke, Tim Laux, Andrea Poiatti
We consider a quasilinear Allen--Cahn system which arises when the gradient energy term in the Ginzburg--Landau energy also contains zero order terms. Such systems offer significan…
Analysis of a Cahn-Hilliard-Canham-Helfrich system for the evolution of a two-phase membrane
Harald Garcke, Mathias Wilke
The coupling of the evolution of a surface with evolution equations defined on that surface is of relevance in many applications and has been in the focus of interest in the analys…
On a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities: Energy equality and Lyapunov stability
Harald Garcke, Maoyin Lv, Hao Wu
We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded do…
A convergent finite element method for two-phase Stokes flow driven by surface tension
Genming Bai, Harald Garcke, Shravan Veerapaneni
We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in , , with interface dynamics gov…
Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves
Genming Bai, Harald Garcke, Shravan Veerapaneni
In this paper, we propose a Barrett-Garcke-Nurnberg (BGN) method for evolving geometries under general flows and present the corresponding convergence analysis. Specifically, we ex…
Error estimates for a surface finite element method for anisotropic mean curvature flow
Klaus Deckelnick, Harald Garcke, Balázs Kovács
Error estimates are proved for an evolving surface finite element semi-discretization for anisotropic mean curvature flow of closed surfaces. For the geometric surface flow, a syst…
Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
Helmut Abels, Harald Garcke, Julia Wittmann
The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transitio…
On a diffuse interface model for diblock copolymers interacting with an electric field
Helmut Abels, Andrea Di Primio, Harald Garcke
We consider a diffuse interface model describing a ternary system constituted by a conductive diblock copolymer and a homopolymer acting as solvent. The resulting dynamics is model…
Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness
Helmut Abels, Harald Garcke, Andrea Poiatti
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and…
Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
Helmut Abels, Harald Garcke, Andrea Poiatti
A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard…