Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High order two dimensional nonoscillatory methods for solving Hamilton-Jacobi scalar equations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Analysis of the discontinuous Galerkin method for Hamilton—Jacobi equations
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes
Journal of Scientific Computing
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
SIAM Journal on Scientific Computing
High-Order Central WENO Schemes for Multidimensional Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
Hi-index | 7.29 |
In this paper, a class of weighted essentially non-oscillatory (WENO) schemes with a Lax-Wendroff time discretization procedure, termed WENO-LW schemes, for solving Hamilton-Jacobi equations is presented. This is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge-Kutta time discretizations. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with the original WENO with Runge-Kutta time discretizations schemes (WENO-RK) of Jiang and Peng [G. Jiang, D. Peng, Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 2126-2143] for Hamilton-Jacobi equations, the major advantages of WENO-LW schemes are more cost effective for certain problems and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.