On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: Energy conservation and multi-symplecticity

JOURNAL OF COMPUTATIONAL PHYSICS

卷:419

Article

Sun, Zheng¹  Xing, Yulong¹ 

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

关键词: Discontinuous Galerkin methods;    Hamiltonian partial differential equations;    Multi-symplecticity;    Energy conservation;   

DOI  :  10.1016/j.jcp.2020.109662

来源: Elsevier

【 摘 要 】

In this paper, we present and study discontinuous Galerkin ( DG) methods for onedimensional multi-symplectic Hamiltonian partial differential equations. We particularly focus on semi-discrete schemes with spatial discretization only, and show that the proposed DG methods can simultaneously preserve the multi-symplectic structure and energy conservation with a general class of numerical fluxes, which includes the wellknown central and alternating fluxes. Applications to the wave equation, the BenjaminBona-Mahony equation, the Camassa-Holm equation, the Korteweg-de Vries equation and the nonlinear Schrodinger equation are discussed. Some numerical results are provided to demonstrate the accuracy and long time behavior of the proposed methods. Numerically, we observe that certain choices of numerical fluxes in the discussed class may help achieve better accuracy compared with the commonly used ones including the central fluxes. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free