A new class of parametric finite element methods, with a new type of artificial tangential
velocity constructed at the continuous level, is proposed for solving surface evolution under …

We propose a structure-preserving parametric finite element method (SP-PFEM) for
discretizing the surface diffusion of a closed curve in two dimensions (2D) or a surface in …

An artificial tangential velocity is introduced into the evolving finite element methods for
mean curvature flow and Willmore flow proposed by Kovács et al.(Numer Math 143 (4), 797 …

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 …

Parametric finite element methods have achieved great success in approximating the
evolution of surfaces under various different geometric flows, including mean curvature flow …

We propose and analyze volume-preserving parametric finite element methods for surface
diffusion, conserved mean curvature flow and an intermediate evolution law in an …

We deal with a long-standing problem about how to design an energy-stable numerical
scheme for solving the motion of a closed curve under anisotropic surface diffusion with a …

A proof of convergence is given for a novel evolving surface finite element semi-
discretization of Willmore flow of closed two-dimensional surfaces, and also of surface …

We study the dynamics of a small solid particle arising from the dewetting of a thin film on a
curved substrate driven by capillarity, where mass transport is controlled by surface …

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 …