Free Boundary Problems 2026

Session

Thin Material Structures

MS-11

7 Sept 2026, 14:00

Humboldt Universität zu Berlin

Conveners

Thin Material Structures: MS-11-1

• Axel Voigt

Thin Material Structures: MS-11-2

• Weizhu Bao (National University of Singapore)

Description

Organisers: Weizhu Bao, Axel Voigt

107. Sharp Interface Models for Solid-State Dewetting Problems

Prof. Weizhu Bao (National University of Singapore)

07/09/2026, 14:00

Thin Material Structures

In this talk, I will present sharp interface models with anisotropic surface energy for simulating solid-state dewetting and the morphological evolution of patterned islands on a substrate. We will show how to derive the sharp interface model via thermovariation dynamics, i.e. variation of the interfacial energy via an open curve with two triple points moving along a fixed substrate. The sharp...

26. Convergence of finite elements for a bulk-surface coupled free boundary problem

Yifei Li (Tuebingen University)

07/09/2026, 14:30

Thin Material Structures

In this talk, we present a numerical analysis of the Eyles-King-Styles tumor growth model, a free boundary problem coupling a Poisson equation in the bulk \Omega with a forced mean curvature flow on its boundary \Gamma. Unlike existing evolving surface analyses based on integer-order Sobolev spaces, this bulk-surface coupling requires H^{1/2}-order regularity on \Gamma. We establish a...

31. A Multi-Phase-Field Approach to Solid-State Dewetting of Polycrystalline Thin Films

Marco Salvalaglio (TU Dresden)

07/09/2026, 15:00

Thin Material Structures

Solid-state dewetting is the process through which thin solid films break and retract on a substrate, leading to the formation of nanostructures. Dewetting in single-crystalline films is well understood as a surface-energy-driven phenomenon governed by surface diffusion. Polycrystalline films, by contrast, exhibit additional complexity due to the presence of extended defects (grain boundaries)...

64. Optimal L² error analysis of a loosely coupled finite element scheme for thin-structure interactions

Prof. Buyang Li (The Hong Kong Polytechnic University)

07/09/2026, 15:30

Thin Material Structures

Finite element methods and kinematically coupled schemes that decouple the fluid velocity and structure displacement have been extensively studied for incompressible fluid-structure interaction (FSI) over the past decade. While these methods are known to be stable and easy to implement, optimal error analysis has remained challenging. Previous work has primarily relied on the classical...

106. Self-avoiding Fluid Deformable Surfaces

Maik Porrmann (Dresden University of Technology)

08/09/2026, 10:30

Thin Material Structures

We propose a numerical method for fluid deformable surfaces governed by surface Stokes flow and Helfrich bending energy under active growth, aiming to model shape evolution of the epithelium sheets in developmental processes. As a new extension of the model, we prevent self-intersections, which commonly arise under large deformations or low enclosed volume to area ratios, by incorporating the...

59. Numerical Simulation of Fluid Deformable Surfaces in Stream Function Formulation

Enno Igel (TU Dresden)

08/09/2026, 11:00

Thin Material Structures

We consider the surface Stokes-Helfrich problem using a stream function formulation. The formulation is considered for simply connected surfaces without boundary. It is based on a splitting of the velocity field in normal and tangential components and the Helmholtz decomposition of the tangential part. For its numerical solution the surface is approximated by higher order isoparametric...

54. Vorticity-Homology and Variational Formulations for Navier--Stokes and Scriven Flows on Surfaces with Arbitrary Topology

Albert Chern (University of California San Diego)

08/09/2026, 11:30

Thin Material Structures

Scalar vorticity formulation for fluid equations on surfaces is computationally attractive. However, the vorticity equation is incomplete on a non-simply-connected surface. We derive a new evolution equation for the finite dimensional harmonic (cohomology) components of the flow. We also show that the vorticity equation has a curvature-dependent, vorticity production term in addition to the...

20. Surface Beris-Edwards-Helfrich models - how local orientational order can influence global shape

Axel Voigt

08/09/2026, 12:00

Thin Material Structures

We consider general models for hydrodynamic surface liquid crystals on (self-)evolving surfaces. We focus on nematic liquid crystals and model them using a Q-tensor approach. The model will be derived using the Lagrange-d´Alambert principle. Our Q-tensor is a 3D object defined on the surface. Here we address specific forms, essentially "surface conforming" Q-tensors, with eigenvectors in...