  This paper focuses on the adaptive discontinuous Galerkin (DG) methods for
the tempered fractional (convection) diffusion equations. The DG schemes with
interior penalty for the diffusion term and numerical flux for the convection
term are used to solve the equations, and the detailed stability and
convergence analyses are provided. Based on the derived posteriori error
estimates, the local error indicator is designed. The theoretical results and
the effectiveness of the adaptive DG methods are respectively verified and
displayed by the extensive numerical experiments. The strategy of designing
adaptive schemes presented in this paper works for the general PDEs with
fractional operators.
