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
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
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
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
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
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)
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
A technique of treating negative weights in WENO schemes
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 schemes for Hamilton-Jacobi equations on triangular meshes
Journal of Computational and Applied Mathematics
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics
Journal of Scientific Computing
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In this paper, we extend a class of the Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the Hamilton-Jacobi equations by Qiu and Shu (2005) [24] to two dimensional unstructured meshes. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first two derivative values are evolved via time advancing and used in the reconstructions, while only the function values are evolved and used in the original WENO schemes which are nodal based approximations. The third and fourth order HWENO schemes using the combinations of second order approximations with nonlinear weights and TVD Runge-Kutta time discretization method are used here. Comparing with the original WENO schemes for Hamilton-Jacobi equations, one major advantage of HWENO schemes presented here is its compactness in the reconstructions. Extensive numerical tests are performed to illustrate the capability and high order accuracy of the methodologies.