High-resolution semi-discrete Hermite central-upwind scheme for multidimensional Hamilton-Jacobi equations

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• 作者：Li Cai^a ; ^{caili@nwpu.edu.cn" class="auth_mail} ; Wenxian Xie^a ; Yufeng Nie^a ; Jianhu Feng^b
• 关键词：Hamilton&ndash ; Jacobi equations ; Semi-discrete central-upwind scheme ; Hermite interpolation
• 刊名：Applied Numerical Mathematics
• 出版年：June, 2014
• 年：2014
• 卷：80
• 期：Complete
• 页码：22-45
• 全文大小：4756 K

文摘

We introduce a high resolution fifth-order semi-discrete Hermite central-upwind scheme for multidimensional Hamilton-Jacobi equations. The numerical fluxes of the scheme are constructed by Hermite polynomials which can be obtained by using the short-time assignment of the first derivatives. The extensions of the proposed semi-discrete Hermite central-upwind scheme to multidimensional cases are straightforward. The accuracy, efficiency and stability properties of our schemes are finally demonstrated via a variety of numerical examples.