Virtual element method for the Sobolev equations

被引：5
作者：
Zhang, Buying [1 ,2 ]
Zhao, Jikun [3 ]
Chen, Shaochun [3 ]
机构：
[1] Hebei Normal Univ Sci & Technol, Sch Math & Informat Sci & Technol, Qinhuangdao, Hebei, Peoples R China
[2] Yanshan Univ, Sch Econ & Management, Qinhuangdao, Hebei, Peoples R China
[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 01期
关键词：
error bounds; polygonal meshes; Sobolev equations; stability and convergence; virtual element method; SUPERCONVERGENCE;
D O I：
10.1002/mma.8579
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The virtual element method for the Sobolev equations is proposed in this paper, where the semi-discrete scheme and the fully discrete scheme are both discussed. With the help of the energy projection operator defined by the discrete bilinear form, the corresponding optimal error estimates in the L2$$ {L}<^>2 $$ norm and H1$$ {H}<^>1 $$ semi-norm for both the semi-discrete solution and the fully discrete solution are deduced. Finally, three numerical examples are carried out to verify the theoretical results.
引用
收藏
页码：1266 / 1281
页数：16
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