A fifth-order WENO scheme with arc-length smoothness indicators based on exponential polynomials for Hamilton-Jacobi equations

In this paper, the authors introduce a new Weighted Essentially Nonoscillatory (WENO) scheme. This scheme is founded on exponential functions and utilizes arc-length smoothness indicators. The primary purpose of this WENO scheme is to provide accurate approximations for the viscosity numerical solutions of Hamilton-Jacobi equations. The arc-length smoothness indicators are derived from the derivatives of reconstructed polynomials within each sub-stencil. These smoothness indicators play a crucial role in approximating the viscosity numerical solutions of Hamilton-Jacobi equations, ensuring high-resolution results and minimizing absolute truncation errors. Numerous numerical tests have been carried out and presented to demonstrate the performance capabilities and numerical accuracy of the proposed scheme, comparing it to several traditional WENO schemes.