A Mixed Discontinuous Galerkin Method for the Helmholtz Equation. (4th May 2020)

• Record Type: Journal Article
• Authors: Hu, Qingjie; He, Yinnian; Li, Tingting; Wen, Jing
• Other Names: Cheng Yumin Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-05-04
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/9582583
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we introduce and analyze a mixed discontinuous Galerkin method for the Helmholtz equation. The mixed discontinuous Galerkin method is designed by using a discontinuous P p + 1 − 1 − P p − 1 finite element pair for the flux variable and the scattered field with p ≥ 0 . We can get optimal order convergence for the flux variable in both H div -like norm and L 2 norm and the scattered field in L 2 norm numerically. Moreover, we conduct the numerical experiments on the Helmholtz equation with perturbation and the rectangular waveguide, which also demonstrate the good performance of the mixed discontinuous Galerkin method.