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We proposed a structure-preserving stabilized parametric finite element method (SPFEM) for the evolution of closed curves under anisotropic surface diffusion with an arbitrary surface energy $\hat{\gamma}(\theta)$. By introducing a…

Numerical Analysis · Mathematics 2024-04-03 Yulin Zhang , Yifei Li , Wenjun Ying

The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…

Numerical Analysis · Computer Science 2009-09-30 G. Haikal

In this work, we consider the three-dimensional solid-state dewetting with strongly anisotropic surface energy, assuming an axisymmetric morphology of the thin film. However, when surface energy exhibits strong anisotropy, certain…

Numerical Analysis · Mathematics 2025-01-09 Meng Li , Chunjie Zhou

We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…

Numerical Analysis · Mathematics 2026-02-23 Tokuhiro Eto , Harald Garcke , Robert Nürnberg

We consider the problem of electrowetting on dielectric (EWoD). The system involves the dynamics of a conducting droplet, which is immersed in another dielectric fluid, on a dielectric substrate under an applied voltage. The fluid dynamics…

Computational Physics · Physics 2021-03-17 Quan Zhao , Weiqing Ren

In this work, we consider the solid-state dewetting of an axisymmetric thin film on a curved-surface substrate, with the assumption that the substrate morphology is also axisymmetric. Under the assumptions of axisymmetry, the surface…

Numerical Analysis · Mathematics 2025-01-03 Zhenghua Duan , Meng Li , Chunjie Zhou

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…

Numerical Analysis · Mathematics 2022-11-07 Weizhu Bao , Harald Garcke , Robert Nürnberg , Quan Zhao

We propose a sharp-interface continuum model based on a thermodynamic variational approach to investigate the strong anisotropic effect on solid-state dewetting including contact line dynamics. For sufficiently strong surface energy…

Materials Science · Physics 2017-01-10 Wei Jiang , Yan Wang , Quan Zhao , David J. Srolovitz , Weizhu Bao

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…

Numerical Analysis · Mathematics 2018-05-14 Stephen Edward Moore

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 spatially inhomogeneous and anisotropic surface energy…

Numerical Analysis · Mathematics 2025-06-09 Harald Garcke , Robert Nürnberg

A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem…

Fluid Dynamics · Physics 2015-06-04 James Sprittles , Yulii Shikhmurzaev

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

In this paper we present a finite element method (FEM) for two-phase incompressible flows with moving contact lines. We use a sharp interface Navier-Stokes model for the bulk phase fluid dynamics. Surface tension forces, including Marangoni…

Fluid Dynamics · Physics 2015-10-13 A. Reusken , X. Xu , L. Zhang

In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He

This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described…

Computational Engineering, Finance, and Science · Computer Science 2022-01-05 Mostafa Faraji , Alexander Seitz , Christoph Meier , Wolfgang A. Wall

Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…

Numerical Analysis · Mathematics 2018-05-15 Christoph Erath , Robert Schorr

For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy $\gamma(\boldsymbol{n})$ in three dimensions (3D), where $\boldsymbol{n}$ is the unit outward normal vector, by introducing…

Numerical Analysis · Mathematics 2022-11-01 Weizhu Bao , Yifei Li

This paper addresses a two-dimensional sharp interface variational model for solid-state dewetting of thin films with surface energies, introduced by Wang, Jiang, Bao, and Srolovitz in \cite{jiang2016solid}. Using the $H^{-1}$-gradient flow…

Analysis of PDEs · Mathematics 2024-12-16 Gianni Dal Maso , Irene Fonseca , Giovanni Leoni

Dewetting of liquid films on solid surfaces in the presence of evaporation is a common phenomenon and has been studied by many researchers. The previous numerical approach has revealed that evaporation accelerates the dewetting speed of the…

Soft Condensed Matter · Physics 2023-05-16 Xiaolong Zhang , Vadim Nikolayev