We extend the symmetrized parametric finite method for the evolution of a closed curve
under anisotropic surface diffusion in two dimensions, recently proposed by us [W. Bao, W …

Over the last two decades, the field of geometric curve evolutions has attracted significant
attention from scientific computing. One of the most popular numerical methods for solving …

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 …

We propose a novel class of temporal high-order parametric finite element methods for
solving a wide range of geometric flows of curves and surfaces. By incorporating the …

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 …

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 …

We consider parametric finite element approximations for the anisotropic surface diffusion
flow in an axisymmetric setting. Based on the anisotropy function, we introduce a symmetric …

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 …

We propose and analyze a structure-preserving parametric finite element method (SP-
PFEM) for the evolution of a closed curve under different geometric flows with arbitrary …

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 …