无外在稳定的虚拟元素方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Numerical Analysis Pub Date : 2024-02-20 DOI:10.1137/22m1504196

Chunyu Chen, Xuehai Huang, Huayi Wei

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 1 期第 567-591 页，2024 年 2 月。摘要。针对二阶椭圆问题开发了任意多项式度下无外在稳定的虚元方法（VEM），包括任意维度下的非顺应虚元方法和顺应虚元方法。关键在于构造局部[math]符合宏有限元空间，使得虚拟元素函数梯度的相关[math]投影是可计算的，并且[math]投影在[math]规范中对虚拟元素函数空间的梯度具有均匀下界。推导出了这些虚元函数的最佳误差估计值。还提供了数值实验来测试无外在稳定的 VEM。

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Virtual Element Methods Without Extrinsic Stabilization

SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 567-591, February 2024.
Abstract. Virtual element methods (VEMs) without extrinsic stabilization in an arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local [math]-conforming macro finite element spaces such that the associated [math] projection of the gradient of virtual element functions is computable, and the [math] projector has a uniform lower bound on the gradient of virtual element function spaces in the [math] norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization.

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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.