发表机构
ICMSEC, State Key Laboratory of Mathematical Sciences (SKLMS), Academy of Mathematics and Systems Science, and School of Mathematical Science, University of Chinese Academy of Sciences, Chinese Academy of Sciences（中国科学院数学与系统科学研究院，中国科学院大学数学科学学院，数学科学重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种针对含三次非线性与高阶导数项的修正Camassa–Holm方程的局部间断Galerkin方法，该方法可实现能量守恒与稳定性，误差估计严谨，数值算例表明其能捕捉方程的peakon解。
AI 中文摘要
本文针对含三次非线性项与高阶导数项的修正Camassa–Holm（mCH）方程，提出一种局部间断Galerkin（LDG）方法。该方法分别采用守恒型数值通量与耗散型数值通量，实现能量守恒与稳定性，同时建立了半离散格式的误差估计。数值算例验证了理论结果的严谨性，且所提LDG方法能够捕捉mCH方程的peakon解。
英文摘要
In this paper, we propose a local discontinuous Galerkin (LDG) method for the modified Camassa-Holm (mCH) equation that contains cubic nonlinearity and high-order derivative terms. Energy conservation and stability are obtained using the conservative and dissipative fluxes, respectively. The error estimate of the semi-discrete scheme is also established. Numerical examples verify that our theoretical findings are sharp and the proposed LDG method is capable of capturing the peakon solution of the mCH equation.
Comments28 pages, 14 figures
