Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations (Journal of Computational Mathematics, 2021)
This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penaltyfor the diffusion term and numerical flux for the convection term are used to solve theequations, and the detailed stability and convergence analyses are provided. Based onthe derived posteriori error estimates, the local error indicator is designed. The theoretical results and the effectiveness of the adaptive DG methods are, respectively, verifiedand displayed by the extensive numerical experiments. The strategy of designing adaptiveschemes presented in this paper works for the general PDEs with fractional operators.
Keywords: Adaptive DG methods; Tempered fractional equations; Posteriori error estimate.