188 citations · 1.6k across the 107 of their papers we have counts for
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Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches
Harald Garcke, Wei Jiang, Chunmei Su +1
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order…
A variational front-tracking method for multiphase flow with triple junctions
Harald Garcke, Robert Nürnberg, Quan Zhao
We present and analyze a variational front-tracking method for a sharp-interface model of multiphase flow. The fluid interfaces between different phases are represented by curve ne…
Complex pattern formation governed by a Cahn-Hilliard-Swift-Hohenberg system: Analysis and numerical simulations
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting syst…
Parametric finite element approximation of two-phase Navier--Stokes flow with viscoelasticity
Harald Garcke, Robert Nürnberg, Dennis Trautwein
In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navi…
A finite element method for anisotropic crystal growth on surfaces
Harald Garcke, Robert Nürnberg
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a…
Existence of Weak Solutions to a Cahn-Hilliard-Biot System
Helmut Abels, Harald Garcke, Jonas Haselböck
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearl…