TY - JOUR
T1 - Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations
AU - Wang , Xudong
AU - Deng , Weihua
JO - Journal of Computational Mathematics
VL - 6
SP - 839
EP - 867
PY - 2020
DA - 2020/06
SN - 38
DO - http://doi.org/10.4208/jcm.1906-m2019-0040
UR - https://global-sci.org/intro/article_detail/jcm/16970.html
KW - Adaptive DG methods, Tempered fractional equations, Posteriori error estimate.
AB - <p style="text-align: justify;">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.</p>