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
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
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
A MUSCL method satisfying all the numerical entropy inequalities
Mathematics of Computation
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
Journal of Computational Physics
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
Journal of Computational Physics
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
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
On the Numerical Approximation of First-Order Hamilton-Jacobi Equations
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes
Journal of Computational Physics
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
Hi-index | 31.46 |
In this paper, a class of weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving Hamilton-Jacobi equations is presented. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. Comparing with the original WENO schemes of Jiang and Peng [Weighted ENO schemes for Hamilton-Jacobi equations, SIAM Journal on Scientific Computing 21 (2000) 2126] for Hamilton-Jacobi equations, one major advantage of HWENO schemes is its compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.