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Volume 28, Issue 5
Dissipative Numerical Methods for the Hunter-Saxton Equation

Yan Xu & Chi-Wang Shu

DOI: 10.4208/jcm.1003-m0003

J. Comp. Math., 28 (2010), pp. 606-620.

Published online: 2010-10

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  • Abstract

In this paper, we present further development of the local discontinuous Galerkin (LDG) method designed in [21] and a new dissipative discontinuous Galerkin (DG) method for the Hunter-Saxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].

  • Keywords

Discontinuous Galerkin method, Local discontinuous Galerkin method, dissipation, Hunter-Saxton equation, Stability.

  • AMS Subject Headings

65M60, 37K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-606, author = {}, title = {Dissipative Numerical Methods for the Hunter-Saxton Equation}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {5}, pages = {606--620}, abstract = {

In this paper, we present further development of the local discontinuous Galerkin (LDG) method designed in [21] and a new dissipative discontinuous Galerkin (DG) method for the Hunter-Saxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1003-m0003}, url = {http://global-sci.org/intro/article_detail/jcm/8540.html} }
TY - JOUR T1 - Dissipative Numerical Methods for the Hunter-Saxton Equation JO - Journal of Computational Mathematics VL - 5 SP - 606 EP - 620 PY - 2010 DA - 2010/10 SN - 28 DO - http://doi.org/10.4208/jcm.1003-m0003 UR - https://global-sci.org/intro/article_detail/jcm/8540.html KW - Discontinuous Galerkin method, Local discontinuous Galerkin method, dissipation, Hunter-Saxton equation, Stability. AB -

In this paper, we present further development of the local discontinuous Galerkin (LDG) method designed in [21] and a new dissipative discontinuous Galerkin (DG) method for the Hunter-Saxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].

Yan Xu & Chi-Wang Shu. (1970). Dissipative Numerical Methods for the Hunter-Saxton Equation. Journal of Computational Mathematics. 28 (5). 606-620. doi:10.4208/jcm.1003-m0003
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