Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation

作     者：Limei Li Da Xu 

作者机构：College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China Department of MathematicsHunan Institute of Science and TechnologyYueyang 414000China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2014年第7卷第1期

页      面：41-57页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The authors would like to thank the referees for their valuable comments and suggestions This work was supported by the National Natural Science Foundation of China,contract grant number 11271123 

主　　题：Fractional evolution equation alternating direction implicit method Galerkin finite element method backward Euler 

摘      要：New numerical techniques are presented for the solution of the twodimensional time fractional evolution equation in the unit *** these methods,Galerkin finite element is used for the spatial discretization,and,for the time stepping,new alternating direction implicit(ADI)method based on the backward Euler method combined with the first order convolution quadrature approximating the integral term are *** ADI Galerkin finite element method is proved to be convergent in time and in the L2 norm in *** convergence order is O(k|ln k|+h^(r)),where k is the temporal grid size and h is spatial grid size in the x and y directions,*** results are presented to support our theoretical analysis.