188 citations · 1.6k across the 107 of their papers we have counts for
9 papers · 1 filter
A structure-preserving finite element method for the multi-phase Mullins-Sekerka problem with triple junctions
Tokuhiro Eto, Harald Garcke, Robert Nürnberg
We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of…
Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities
Helmut Abels, Harald Garcke, Andrea Poiatti
We analyze a diffuse interface model for multi-phase flows of incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smoot…
Approximation and existence of a viscoelastic phase-field model for tumour growth in two and three dimensions
Harald Garcke, Dennis Trautwein
In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport p…
Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow
Harald Garcke, Robert Nürnberg, Quan Zhao
We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving flui…
The anisotropic Cahn--Hilliard equation: regularity theory and strict separation properties
Harald Garcke, Patrik Knopf, Julia Wittmann
The Cahn--Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case with the relevant logarith…
Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures
Harald Garcke, Paul Hüttl, Christian Kahle +1
We consider an optimization problem for the eigenvalues of a multi-material elastic structure that was previously introduced by Garcke et al. [Adv. Nonlinear Anal. 11 (2022), no. 1…