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  最后修改时间: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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