平均曲率流的动态Ritz投影与参数有限元的最优收敛

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-07-14 DOI:10.1137/24m1689053

Buyang Li, Rong Tang

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第4期，1454-1481页，2025年8月。摘要。提出了一种新的方法来研究三维空间中封闭曲面平均曲率流的参数化有限元逼近的收敛性。在这种方法中，通过将数值解与本文引入的平均曲率流的动态Ritz投影进行比较，而不是将文献中常用的平均曲率流插值进行误差分析。在[math]和[math]规范中建立了与动态里兹投影有关的近似平均曲率流的误差。利用这些结果，证明了[数学]范数中封闭曲面平均曲率流的参数有限元方法的最优收敛性，包括分段线性有限元的参数有限元方法的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dynamic Ritz Projection of Mean Curvature Flow and Optimal [math] Convergence of Parametric FEM

SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1454-1481, August 2025.
Abstract. A new approach is developed to study the convergence of parametric finite element approximations to the mean curvature flow of closed surfaces in three-dimensional space. In this approach, the error analysis is conducted by comparing the numerical solution to a dynamic Ritz projection of the mean curvature flow introduced in this paper rather than an interpolation of the mean curvature flow, as commonly used in the literature. The errors associated with the dynamic Ritz projection in approximating the mean curvature flow are established in the [math] and [math] norms. Leveraging these results, optimal-order convergence of parametric finite element methods for mean curvature flow of closed surfaces in the [math] norm is proved, including the convergence of parametric finite element methods with piecewise linear finite elements.

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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.