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AbstractIn [35,36], we presented an h-adaptive Runge-Kutta discontinuous Galerkin method using troubled-cell indicators for solving hyperbolic conservation laws. A tree data structure (binary tree in one dimension and quadtree in two dimensions) is used to aid storage and neighbor finding. Mesh adaptation is achieved by refining the troubled cells and coarsening the untroubled “children”. Extensive numerical tests indicate that the proposed h-adaptive method is capable of saving the computational cost and enhancing the resolution near the discontinuities. In this paper, we apply this h-adaptive method to solve Hamilton-Jacobi equations, with an objective of enhancing the resolution near the discontinuities of the solution derivatives. One- and two-dimensional numerical examples are shown to illustrate the capability of the method.

In this work, we study the strong decay of the newly observed Pcs(4459), assuming that it is a pure molecular state. Considering two possible spin-parity assignments JP= 1/2−and JP= 3/2−, the partial decay widths of the molecular state into J/ψΛ, Ds−Λc+, and final states through hadronic loops are evaluated with the help of the effective Lagrangians. In comparison with the LHCb data, the S-wave molecular with JP= 1/2−assignment for Pcs(4459) is supported by our study, while the Pcs(4459) in spin-parity JP= 3/2−case may be explained as an S-wave coupled bound state with lager component. In addition, the calculated partial decay widths with JP= 1/2−molecular state picture indicate that allowed decay mode, , may have the biggest branching ratio. The experimental measurements for this strong decay process could be a crucial test for the molecule interpretation of the Pcs(4459).