| Energy-Preserving $H^1$--Galerkin Schemes for the Hunter-Saxton Equation |
| Received:October 30, 2016 Revised:December 02, 2016 |
| Key Words:
Hunter-Saxton equation energy-preservation Galerkin methods
|
| Fund Project: |
| Author Name | Affiliation | | Yuto MIYATAKE | Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan | | 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 |
|
| Hits: 3522 |
| Download times: 2277 |
| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.01.010 |
| View Full Text View/Add Comment |
|
|
|
