Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes

被引：8
|
作者：
Meng, Jian [1 ]
Wang, Gang [2 ]
Mei, Liquan [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
[2] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2023年 / 43卷 / 03期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
mixed virtual element method; transmission eigenvalue problem; spectral approximation; error estimates; EXISTENCE;
D O I：
10.1093/imanum/drac019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we propose and analyze a mixed virtual element method for the Helmholtz transmission eigenvalue problem, which is a fourth order, nonlinear and non-self-adjoint eigenvalue problem and is important in the inverse scattering theory. The conforming virtual element is used for discretization. We prove correct spectral approximation and error estimates of the discrete scheme. Finally, we show several numerical examples to verify the theoretical results and present the performance of different stabilization parameters and the comparison with the C-1 virtual element method.
引用
收藏
页码：1685 / 1717
页数：33
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