封闭表面轴对称Willmore流的能量稳定参数有限元逼近

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2025-04-02 DOI:10.1016/j.jcp.2025.113977

Cuiling Ma, Xufeng Xiao, Xinlong Feng

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引用次数: 0

摘要

本文提出并分析了封闭表面轴对称Willmore流的能量稳定近似。这种方法扩展了Bao和Li[4]关于平面Willmore曲线流的原始工作。通过各种几何量之间的关系，导出了轴对称Willmore流的等效几何方程组，包括参数化演化方程和平均曲率演化方程。该方法由空间上的线性参数有限元法和时间上的倒推欧拉法组成。进一步证明了完全离散格式是无条件能量稳定的。采用Newton-Raphson迭代法求解非线性系统。最后，通过数值算例说明了该方法在轴对称条件下的效率和能量稳定性。

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An energy-stable parametric finite element approximation for axisymmetric Willmore flow of closed surfaces

In this paper, we propose and analyze an energy-stable approximation for axisymmetric Willmore flow of closed surfaces. This approach extends the original work of Bao and Li [4] for the planar Willmore flow of curves. Through relations among various geometric quantities, we derive a system of equivalent geometric equations for the axisymmetric Willmore flow, including the evolution equations for the parameterization and mean curvature. The proposed method consists of the linear parametric finite element method in space and the backward Euler method in time. Furthermore, we prove that the fully discrete scheme is unconditionally energy-stable. The Newton-Raphson iteration method is adopted to solve the nonlinear system. Finally, numerical examples are presented to illustrate the efficiency and energy stability of the proposed method for Willmore flow in an axisymmetric setting.

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来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.