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The selection of time step plays a crucial role in improving stability andefficiency in the Discontinuous Galerkin (DG) solution of hyperbolicconservation laws on adaptive moving meshes that typically employs explicitstepping. A commonly used selection of time step is a direct extension based onCourant-Friedrichs-Levy (CFL) conditions established for fixed and uniformmeshes. In this work, we provide a mathematical justification for those timestep selection strategies used in practical adaptive DG computations. Astability analysis is presented for a moving mesh DG method for linear scalarconservation laws. Based on the analysis, a new selection strategy of the timestep is proposed, which takes into consideration the coupling of the$\alpha$-function (that is related to the eigenvalues of the Jacobian matrix ofthe flux and the mesh movement velocity) and the heights of the mesh elements.The analysis also suggests several stable combinations of the choices of the$\alpha$-function in the numerical scheme and in the time step selection.Numerical results obtained with a moving mesh DG method for Burgers' and Eulerequations are presented. For comparison purpose, numerical results obtainedwith an error-based time step-size selection strategy are also given.

A study on CFL conditions for the DG solution of conservation laws on adaptive moving meshes