Skip to content
DraconiticResearch
Search Sources API
194,220 studies31 sourcesUpdated 26 min ago
PreprintCC BY 4.0arXiv

A Local Discontinuous Galerkin method for the modified Camassa--Holm equation

  • Xiang-Ke Chang
  • Yong Liu
  • Qi Tao
Open at sourcePDFDOICite

Abstract

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.

Related

  1. The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes
    Leilei Wei, Yanping Chen, Fangfang Qin +2
    Applied Numerical MathematicsPeer-reviewedLicence not stated9 citedGeneral mathematicsOpenAlex
  2. An Energy-based discontinuous Galerkin method for the Westervelt equation with absorbing boundary conditions
    Yiwei Wang, Lu Zhang
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. Nonlinear coercivity and orbital stability of smooth solitary waves for the modified Camassa--Holm equation
    Xijun Deng, Ji Li, Zhisu Liu
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv
  4. A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems
    Maurice S. Fabien, Sijing Liu, Marcus Sarkis
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  5. A Discontinuous Galerkin Method for Biharmonic Dirichlet Control Problems With Patch Reconstruction
    Wei Gong, Ruo Li, Jun Yin
    arXivPreprintCC0Full textNumerical analysis & scientific computingOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{chang2026local,
  title = {{A Local Discontinuous Galerkin method for the modified Camassa--Holm equation}},
  author = {Xiang-Ke Chang and Yong Liu and Qi Tao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.28077},
  eprint = {2608.28077},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28077},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Local Discontinuous Galerkin method for the modified Camassa--Holm equation
AU  - Xiang-Ke Chang
AU  - Yong Liu
AU  - Qi Tao
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.28077
UR  - https://arxiv.org/abs/2608.28077
AB  - 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.
ER  -