Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes-Reference-Cited by-同舟云学术

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

Published:2022-05-23 Issue: Volume: Page:
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Meng Jian¹,Wang Gang²,Mei Liquan¹

Affiliation:

1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China

2. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, P.R. China

Abstract

Abstract 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.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

https://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drac019/43796670/drac019.pdf

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