Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry

被引:1
作者
Li, Meng [1 ]
Zhao, Quan [2 ]
机构
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China
基金
中国博士后科学基金; 中国国家自然科学基金;
关键词
Surface diffusion flow; Anisotropy; Parametric finite element method; Axisymmetry; Unconditional stability; Volume conservation; SHARP-INTERFACE MODEL; WILLMORE FLOW; NUMERICAL APPROXIMATION; VARIATIONAL FORMULATION; EVOLUTION-EQUATIONS; ERROR ANALYSIS; MOTION; STABILITY; SCHEME;
D O I
10.1016/j.jcp.2023.112632
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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 positive definite matrix with a suitable stabilizing function. This then gives rise to two novel weak formulations for the axisymmetric flow in terms of the generating curve of the interface. By using piecewise linear elements in space and backward Euler in time, we discretize the weak formulations to obtain different approximating methods. These include a linear approximation which has good mesh properties and nonlinear approximations which can be shown rigorously to satisfy the volume preservation or the unconditional energy stability on the discrete level. Extensive numerical results are reported to demonstrate the accuracy and efficiency of the introduced methods for computing the axisymmetric flow.
引用
收藏
页数:18
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