Virtual Element Methods Without Extrinsic Stabilization

Autor:	Chen, Chunyu, Huang, Xuehai, Wei, Huayi
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis 65N12 65N22 65N30
Druh dokumentu:	Working Paper
Popis:	Virtual element methods (VEMs) without extrinsic stabilization in 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 $H(\textrm{div})$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization. Comment: 26 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.01720 Zobrazit plný text záznamu View this record from Arxiv