WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations

Hermite Weno Schemes with Lax-wendroff Type Time Discretizations for Hamilton-jacobi Equations

In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. 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 are used in the reconstruction...

Hermite WENO schemes for Hamilton–Jacobi equations

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, ...

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes

Article history: Received 1 November 2012 Received in revised form 16 July 2013 Accepted 23 July 2013 Available online 2 August 2013

Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in certain cases. The accuracy and high-resolution properties of our scheme are demonstrated in a variety of nume...