DISCONTINUOUS GALERKIN METHODS AND THEIR ADAPTIVITY FOR THE TEMPERED FRACTION AL(CONVECTION)DIFFUSION EQUATIONS  

作　　者：Xudong Wang Weihua Deng 

机构地区：[1]School of Mathematics and Statistics,Gansu Key Laboratory of Applied Mathematics and Complex Systems,Lanzhou University,Lanzhou 730000,China

出　　处：《Journal of Computational Mathematics》2020年第6期839-867,共29页计算数学（英文）

基　　金：the National Natural Science Foundation of China under grant no.11671182;the Fundamental Research Funds for the Central Universities under grants no.lzujbky-2018-ot03 and no.lzujbky 2019-it17.

摘　　要：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.

关 键 词：Adaptive DG methods Tempered fractional equations Posteriori error estimate 

分 类 号：O17[理学—数学]