High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation  

作　　者：Min Zhang Yang Liu Hong Li 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,Fujian Province,China [2]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China

出　　处：《Communications on Applied Mathematics and Computation》2020年第4期613-640,共28页应用数学与计算数学学报（英文）

基　　金：This work is supported by the National Natural Science Foundation of China(11661058,11761053);the Natural Science Foundation of Inner Mongolia(2017MS0107);the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07).

摘　　要：In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.

关 键 词：Two-dimensional nonlinear fractional difusion equation High-order LDG method Second-orderθscheme Stability and error estimate 

分 类 号：O17[理学—数学]