The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations. (19th August 2020) - Zhang, Rongpei; Liu, Jia; Jiang, Shaohua; Wang, Di
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.