A STRUCTURE-PRESERVING PARAMETRIC FINITE ELEMENT METHOD FOR ANISOTROPIC SURFACE DIFFUSION

Abstract

This thesis aims to develop a SP-PFEM for anisotropic surface diffusion of curves in two dimensions (2D) with d = 2 and of surfaces in three dimensions (3D) with d = 3, incorporating a more general anisotropic surface energy function. The key concepts of the SP-PFEM developed here are the surface energy matrix Zk(n) or Gk(n) and the minimal stabilizing function k0(n). The main contribution of this work is introducing a novel analytical framework that plays a vital role in establishing energy stability, which significantly contributes to the existing PFEMs.