The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations. (19th August 2020)

• Record Type: Journal Article
• Authors: Zhang, Rongpei; Liu, Jia; Jiang, Shaohua; Wang, Di
• Other Names: Yang Zhile Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-08-19
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/8464153
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional second-order wave equation with the periodic boundary conditions. Introducing two auxiliary variables, the second-order equation is rewritten into the first-order equation systems. We prove the stability and energy conservation of this method. By virtue of the generalized Gauss–Radau projection, we can obtain the optimal convergence order in L 2 -norm of O h k + 1 with polynomial of degree k and grid size h . Numerical experiments are given to verify the theoretical results.