A multi-level mixed element scheme of the two-dimensional Helmholtz transmission eigenvalue problem. (29th October 2018)

• Record Type: Journal Article
• Authors: Xi, Yingxia; Ji, Xia; Zhang, Shuo
• Is Part Of: IMA journal of numerical analysis. Volume 40:Number 1(2020)
• Page Start: 686
• Page End: 707
• Publication Date: 2018-10-29
• Subjects: mixed finite element method -- transmission eigenvalue -- multi-level scheme; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry061
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by rectangular grids. We first construct an equivalent linear mixed formulation of the transmission eigenvalue problem and then discretize it with Lagrangian finite elements of low regularities. The proposed scheme admits a natural nested discretization, based on which we construct a multi-level scheme. Optimal convergence rate and optimal computational cost can be obtained with the scheme.