Application of low-dimensional finite element method to fractional diffusion equation  

作　　者：Jincun Liu Hong Li Zhichao Fang Yang Liu 

机构地区：[1]School of Mathematical Sciences Inner Mongolia University Hohhot 010021,P.R.China

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2014年第4期184-200,共17页建模、仿真和科学计算国际期刊（英文）

基　　金：supported by National Natural Science Foundation(Nos.11361035,11361034,11301258);Natural Science Foundation of Inner Mongolia(Nos.2012MS0106,2012MS0108);Scientific Research Projection of Higher Schools of Inner Mongolia(Nos.NJZZ12011,NJZY14013)。

摘　　要：Classical finite element method(FEM)has been applied to solve some fractional differential equations,but its scheme has too many degrees of freedom.In this paper,a low-dimensional FEM,whose number of basis functions is reduced by the theory of proper orthogonal decomposition(POD)technique,is proposed for the time fractional diffusion equation in two-dimensional space.The presented method has the properties of low dimensions and high accuracy so that the amount of computation is decreased and the calculation time is saved.Moreover,error estimation of the method is obtained.Numerical example is given to illustrate the feasibility and validity of the low-dimensional FEM in comparison with traditional FEM for the time fractional differential equations.

关 键 词：Low-dimensional finite element method proper orthogonal decomposition time fractional diffusion equation error estimation 

分 类 号：O17[理学—数学]