High-order schemes for Hamilton-Jacobi equations on triangular meshes

Authors:
Xiang-Gui Li;C. K. Chan
Affiliations:
Beijing Information Technology Institute, Beijing 100101, China;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

Citing 11
Cited 1

Total-variation-diminishing time discretizations

SIAM Journal on Scientific and Statistical Computing
Numerical experiments on the accuracy of ENO and modified ENO schemes

Journal of Scientific Computing
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations

SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading

SIAM Journal on Numerical Analysis
A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations

SIAM Journal on Mathematical 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 Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
Weighted ENO Schemes for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
A technique of treating negative weights in WENO schemes

Journal of Computational Physics

Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes

Journal of Computational Physics

Quantified Score

Hi-index	7.30

Visualization

Abstract

In this paper, two weighted essentially nonoscillatory (ENO) schemes are presented on triangular meshes. By combining quadratic polynomials with weights on the ENO stencil, we construct a scheme with second-order accuracy and another scheme with third-order accuracy. Numerical results show the accuracy and stability of the weighted ENO schemes and resolution for discontinuity.