Convex ENO Schemes for Hamilton-Jacobi Equations

Authors:
Chi-Tien Lin;Xu-Dong Liu
Affiliations:
Department of Applied Mathematics, Providence University, Taichung, Taiwan, Republic of China 43301;Department of Mathematics, UCSB, Santa Barbara, USA
Venue:
Journal of Scientific Computing
Year:
2007

Citing 19
Cited 0

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
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II

Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws

Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations

SIAM Journal on Numerical Analysis
Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids

Journal of Computational Physics
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws

SIAM Journal on Scientific Computing
High-Resolution Nonoscillatory Central Schemes with Nonstaggered Grids for Hyperbolic Conservation Laws

SIAM Journal on Numerical Analysis
Numerical Passage from Systems of Conservation Laws to Hamilton--Jacobi Equations, and Relaxation Schemes

SIAM Journal on Numerical Analysis
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
New high-resolution central schemes for nonlinear conservation laws and convection—diffusion equations

Journal of Computational Physics
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-Resolution Nonoscillatory Central Schemes for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
Strong Stability-Preserving High-Order Time Discretization Methods

SIAM Review
High-Order Central WENO Schemes for Multidimensional Hamilton--Jacobi Equations

SIAM Journal on Numerical Analysis
Adaptive Central-Upwind Schemes for Hamilton---Jacobi Equations with Nonconvex Hamiltonians

Journal of Scientific Computing
Mapped WENO and weighted power ENO reconstructions in semi-discrete central schemes for Hamilton-Jacobi equations

Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In one dimension, viscosity solutions of Hamilton---Jacobi (HJ) equations can be thought as primitives of entropy solutions for conservation laws. Based on this idea, both theoretical and numerical concepts used for conservation laws can be passed to HJ equations even in several dimensions. In this paper, we construct convex ENO (CENO) schemes for HJ equations. This construction is a generalization from the work by Liu and Osher on CENO schemes for conservation laws. Several numerical experiments are performed. L 1 and L 驴 error and convergence rate are calculated as well.