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Virtual Element Methods Without Extrinsic Stabilization
SIAM Journal on Numerical Analysis ( IF 2.9 ) Pub Date : 2024-02-20 , DOI: 10.1137/22m1504196 Chunyu Chen 1 , Xuehai Huang 2 , Huayi Wei 1
SIAM Journal on Numerical Analysis ( IF 2.9 ) Pub Date : 2024-02-20 , DOI: 10.1137/22m1504196 Chunyu Chen 1 , Xuehai Huang 2 , Huayi Wei 1
Affiliation
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.
中文翻译：
无外部稳定的虚拟元素方法
《SIAM 数值分析杂志》，第 62 卷，第 1 期，第 567-591 页，2024 年 2 月。
摘要。针对二阶椭圆问题，开发了在任意多项式中没有外在稳定性的虚拟元素方法（VEM），包括任意维度的非相容 VEM 和相容 VEM。关键是构造局部[数学]一致的宏观有限元空间，使得虚拟单元函数梯度的相关[数学]投影是可计算的，并且[数学]投影仪对虚拟单元的梯度具有统一的下界[数学]范数中的函数空间。针对这些 VEM 得出最佳误差估计。提供了数值实验来测试没有外部稳定的 VEM。
更新日期：2024-02-21
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.
中文翻译：
无外部稳定的虚拟元素方法
《SIAM 数值分析杂志》，第 62 卷，第 1 期，第 567-591 页，2024 年 2 月。
摘要。针对二阶椭圆问题，开发了在任意多项式中没有外在稳定性的虚拟元素方法（VEM），包括任意维度的非相容 VEM 和相容 VEM。关键是构造局部[数学]一致的宏观有限元空间，使得虚拟单元函数梯度的相关[数学]投影是可计算的，并且[数学]投影仪对虚拟单元的梯度具有统一的下界[数学]范数中的函数空间。针对这些 VEM 得出最佳误差估计。提供了数值实验来测试没有外部稳定的 VEM。
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