  In this article, novel smoothness indicators are presented for calculating
the nonlinear weights of weighted essentially non-oscillatory scheme to
approximate the viscosity numerical solutions of Hamilton-Jacobi equations.
These novel smoothness indicators are constructed from the derivatives of
reconstructed polynomials over each sub-stencil. The constructed smoothness
indicators measure the arc-length of the reconstructed polynomials so that the
new nonlinear weights could get less absolute truncation error and gives a
high-resolution numerical solution. Extensive numerical tests are conducted and
presented to show the performance capability and the numerical accuracy of the
proposed scheme with the comparison to the classical WENO scheme.
