A unified structure-preserving parametric finite element method for anisotropic surface diffusion

W Bao, Y Li - Mathematics of Computation, 2024 - ams.org
We propose and analyze a unified structure-preserving parametric finite element method
(SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions $(d= 2) $ and …

A stabilized parametric finite element method for surface diffusion with an arbitrary surface energy

Y Zhang, Y Li, W Ying - Journal of Computational Physics, 2025 - Elsevier
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 …

A structure-preserving parametric finite element method for solid-state dewetting on curved substrates

W Bao, Y Li, Q Zhao - arxiv preprint arxiv:2410.00438, 2024 - arxiv.org
We consider a two-dimensional sharp-interface model for solid-state dewetting of thin films
with anisotropic surface energies on curved substrates, where the film/vapor interface and …

An energy-stable parametric finite element method for the planar Willmore flow

W Bao, Y Li - SIAM Journal on Numerical Analysis, 2025 - SIAM
We propose an energy-stable parametric finite element method (PFEM) for the planar
Willmore flow and establish its unconditional energy stability of the full discretization …

Geometric-structure preserving methods for surface evolution in curvature flows with minimal deformation formulations

G Gao, B Li - Journal of Computational Physics, 2025 - Elsevier
In this article, we design novel weak formulations and parametric finite element methods for
computing surface evolution under mean curvature flow and surface diffusion while …

Energy-stable parametric finite element approximations for regularized solid-state dewetting in strongly anisotropic materials

M Li, C Zhou - arxiv preprint arxiv:2407.04524, 2024 - arxiv.org
In this work, we aim to develop energy-stable parametric finite element approximations for a
sharp-interface model with strong surface energy anisotropy, which is derived from the first …

A structure-preserving parametric finite element method with optimal energy stability condition for anisotropic surface diffusion

Y Li, W Ying, Y Zhang - arxiv preprint arxiv:2501.16660, 2025 - arxiv.org
We propose and analyze a structure-preserving parametric finite element method (SP-
PFEM) for the evolution of closed curves under anisotropic surface diffusion with surface …

Efficient energy-stable parametric finite element methods for surface diffusion flow and applications in solid-state dewetting

M Li, Y Guo, J Bi - arxiv preprint arxiv:2407.09418, 2024 - arxiv.org
Currently existing energy-stable parametric finite element methods for surface diffusion flow
and other flows are usually limited to first-order accuracy in time. Designing a high-order …

Willmore regularized sharp-interface model for strongly anisotropic solid-state dewetting with axisymmetric geometry: modeling and simulation

M Li, C Zhou - arxiv preprint arxiv:2501.04280, 2025 - arxiv.org
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 …

Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies

M Li, C Zhou - arxiv preprint arxiv:2405.05844, 2024 - arxiv.org
Solid-state dewetting (SSD), a widespread phenomenon in solid-solid-vapor system, could
be used to describe the accumulation of solid thin films on the substrate. In this work, we …