WENO scheme with new smoothness indicator for Hamilton–Jacobi equation

In this paper, we develop a new weighted essentially non-oscillatory (WENO) scheme for Hamilton–Jacobi (HJ) equation by proposing a new family of smoothness indicators, which includes the smoothness indicator in Jiang and Peng (2000) as one of its members. The new family of smoothness indicators has three parameters. By choosing the parameters properly, the new WENO scheme provides more accurate numerical solution than the original one, and increases little computational cost.