Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

In this paper we construct high-order weighted essentially nonoscillatory (WENO) schemes for solving the nonlinear Hamilton–Jacobi equations on two-dimensional unstructured meshes. The main ideas are nodal based approximations, the usage of monotone Hamiltonians as building blocks on unstructured meshes, nonlinear weights using smooth indicators of second and higher derivatives, and a strategy ...

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

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

Finite volume Hermite WENO schemes for solving the Hamilton-Jacobi equations II: Unstructured meshes

Abstract. In this paper, we present a new type of Hermite weighted essentially nonoscillatory (HWENO) schemes for solving the Hamilton-Jacobi equations on the finite volume framework. The cell averages of the function and its first one (in one dimension) or two (in two dimensions) derivative values are together evolved via time approaching and used in the reconstructions. And the major advantag...