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Calcolo
Published in: Calcolo 1/2021

01-03-2021

A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem

Authors: Jian Meng, Gang Wang, Liquan Mei

Published in: Calcolo | Issue 1/2021

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Abstract

In this paper, we introduce a \(C^{0}\) virtual element method for the Helmholtz transmission eigenvalue problem, which is a fourth-order non-selfadjoint eigenvalue problem. We consider the mixed formulation of the eigenvalue problem discretized by the lowest-order virtual elements. This discrete scheme is based on a conforming \(H^{1}(\varOmega )\times H^{1}(\varOmega )\) discrete formulation, which makes use of lower regular virtual element spaces. However, the discrete scheme is a non-classical mixed method due to the non-selfadjointness, then we cannot use the framework of classical eigenvalue problem directly. We employ the spectral theory of compact operator to prove the spectral approximation. Finally, some numerical results show that numerical eigenvalues obtained by the proposed numerical scheme can achieve the optimal convergence order.
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Metadata
Title
A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem
Authors
Jian Meng
Gang Wang
Liquan Mei
Publication date
01-03-2021
Publisher
Springer International Publishing
Published in
Calcolo / Issue 1/2021
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-020-00391-5

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