利用人工切向运动的收敛性演化有限元方法，解决规定速度场下的表面演化问题

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-09-17 DOI:10.1137/23m156968x

Genming Bai, Jiashun Hu, Buyang Li

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 5 期第 2172-2195 页，2024 年 10 月。摘要。基于连续问题的新型等效表述，提出了一种新型演化曲面有限元方法，用于计算二维和三维空间中在规定速度场下运动的封闭超曲面的演化。该方法通过使用人工切向运动最小化变形率来提高近似曲面的网格质量。推导出了法向矢量和外韦氏矩阵的传输演化方程，并将其与曲面演化方程耦合，以确保数值近似的稳定性和收敛性。对于阶数为 [math] 的有限元，证明了半离散演化曲面有限元法的优阶收敛性。提供的数值示例说明了所提方法的收敛性及其在改善近似演化曲面网格质量方面的有效性。

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A Convergent Evolving Finite Element Method with Artificial Tangential Motion for Surface Evolution under a Prescribed Velocity Field

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2172-2195, October 2024.
Abstract. A novel evolving surface finite element method, based on a novel equivalent formulation of the continuous problem, is proposed for computing the evolution of a closed hypersurface moving under a prescribed velocity field in two- and three-dimensional spaces. The method improves the mesh quality of the approximate surface by minimizing the rate of deformation using an artificial tangential motion. The transport evolution equations of the normal vector and the extrinsic Weingarten matrix are derived and coupled with the surface evolution equations to ensure stability and convergence of the numerical approximations. Optimal-order convergence of the semidiscrete evolving surface finite element method is proved for finite elements of degree [math]. Numerical examples are provided to illustrate the convergence of the proposed method and its effectiveness in improving mesh quality on the approximate evolving surface.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.