| Yuto MIYATAKE,Geonsik EOM,Tomohiro SOGABE,Shaoliang ZHANG.Energy-Preserving $H^1$--Galerkin Schemes for the Hunter-Saxton Equation[J].数学研究及应用,2017,37(1):107~118 |
| Energy-Preserving $H^1$--Galerkin Schemes for the Hunter-Saxton Equation |
| Energy-Preserving $H^1$--Galerkin Schemes for the Hunter-Saxton Equation |
| 投稿时间：2016-10-30 修订日期：2016-12-02 |
| DOI：10.3770/j.issn:2095-2651.2017.01.010 |
| 中文关键词: Hunter-Saxton equation energy-preservation Galerkin methods |
| 英文关键词:Hunter-Saxton equation energy-preservation Galerkin methods |
| 基金项目: |
| 作者 | 单位 | | Yuto MIYATAKE | Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada, 89154-4020, USA | | Geonsik EOM | Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan | | Tomohiro SOGABE | Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan | | Shaoliang ZHANG | Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan |
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| 中文摘要: |
| We consider the numerical integration of the Hunter--Saxton equation, which models the propagation of weakly nonlinear orientation waves. For the equation, we present two weak forms and their Galerkin discretizations. The Galerkin schemes preserve the Hamiltonian of the equation and can be implemented with cheap $H^1$ elements. Numerical experiments confirm the effectiveness of the schemes. |
| 英文摘要: |
| We consider the numerical integration of the Hunter--Saxton equation, which models the propagation of weakly nonlinear orientation waves. For the equation, we present two weak forms and their Galerkin discretizations. The Galerkin schemes preserve the Hamiltonian of the equation and can be implemented with cheap $H^1$ elements. Numerical experiments confirm the effectiveness of the schemes. |
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