The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations

Rongpei Zhang, Jia Liu, Shaohua Jiang and Di Wang

Complexity, 2020, vol. 2020, 1-9

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 - norm of with polynomial of degree and grid size . Numerical experiments are given to verify the theoretical results.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:8464153

DOI: 10.1155/2020/8464153

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