A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws

In the article [Yang et al. (2012) [37]], the authors have developed a high order moving mesh WENO method for one-dimensional (1D) hyperbolic conservation laws, which is shown to be effective in resolving shocks and other complex solution structures. In this paper, in the light of the similar moving mesh technique, we develop a novel WENO scheme with non-polynomial bases, in particular, the exponential bases to further improve the performance of WENO schemes for solving 1D conservation laws. Furthermore, we modify the original moving mesh technique by developing a new monitor function as well as a different mesh smoothing strategy. A collection of numerical examples is presented to demonstrate high order accuracy and robustness of the method in capturing smooth and non-smooth solutions including the strong δ shock arising from the weakly hyperbolic pressureless Euler equations.