Details

Autor(en) / Beteiligte

• Meng, Jian
• Wang, Gang
• Mei, Liquan

Titel

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

Ist Teil von

• IMA journal of numerical analysis, 2023-05, Vol.43 (3), p.1685-1717

Ort / Verlag

Oxford University Press

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Oxford University Press Journals Current

Beschreibungen/Notizen

• 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.