An energy-stable parametric finite element method for anisotropic surface diffusion

发布时间：2021-06-21 作者：浏览次数：

Speaker:	李逸飞	DateTime:	2021年6月21日（周一）下午16:00-17:00
Brief Introduction to Speaker: 李逸飞，新加坡国立大学。		Place:	六号楼二楼报告厅
Abstract:We propose an energy-stable parametric finite element method (ES-PFEM) to dis- cretize the motion of a closed curve under surface diffusion with an anisotropic surface energy γ(θ) – anisotropic surface diffusion – in two dimensions, while θ is the angle be- tween the outward unit normal vector and the vertical axis. By introducing a positive definite surface energy (density) matrix G(θ), we present a new and simple variational formulation for the anisotropic surface diffusion and prove that it satisfies area/mass conservation and energy dissipation. The variational problem is discretized in space by the parametric finite element method and area/mass conservation and energy dissipation are established for the semi-discretization. Then the problem is further discretized in time by a (semi-implicit) backward Euler method so that only a linear system is to be solved at each time step for the full-discretization and thus it is efficient.