A sixth-order finite difference WENO scheme for Hamilton-Jacobi equations

作者：Cheng, Xiaohan^*; Feng, Jianhu

来源：International Journal of Computer Mathematics, 2019, 96(3): 568-584.

DOI：10.1080/00207160.2018.1447665

• Finite difference method
• Hamilton-Jacobi equations
• WENO scheme
• high order
• upwind scheme

In this paper, a sixth-order finite difference weighted essentially non-oscillatory (WENO) scheme is developed to approximate the viscosity solution of the Hamilton-Jacobi equations. This new WENO scheme has the same spatial nodes as the classical fifth-order WENO scheme proposed by Jiang and Peng [Weighted ENO schemes for Hamilton-Jacobi equations, SIAM. J. Sci. Comput. 21 (2000), pp. 2126-2143] but can be as high as sixth-order accurate in smooth region while keeping sharp discontinuous transitions with no spurious oscillations near discontinuities. Extensive numerical experiments in one- and two-dimensional cases are carried out to illustrate the capability of the proposed scheme.

• 出版日期2019-3-4
• 单位长安大学