典型文献
ANALYSIS OF A MULTI-TERM VARIABLE-ORDER TIME-FRACTIONAL DIFFUSION EQUATION AND ITS GALERKIN FINITE ELEMENT APPROXIMATION
文献摘要：
In this paper,we study the well-posedness and solution regularity of a multi-term variable-order time-fractional diffusion equation,and then develop an optimal Galerkin finite element scheme without any regularity assumption on its true solution.We show that the solution regularity of the considered problem can be affected by the maximum value of variable-order at initial time t=0.More precisely,we prove that the solution to the multi-term variable-order time-fractional diffusion equation belongs to C2([0,T])in time provided that the maximum value has an integer limit near the initial time and the data has sufficient smoothness,otherwise the solution exhibits the same singular behavior like its constant-order counterpart.Based on these regularity results,we prove optimal-order convergence rate of the Galerkin finite element scheme.Furthermore,we develop an efficient parallel-in-time algorithm to reduce the computational costs of the evaluation of multi-term variable-order fractional derivatives.Numerical experiments are put forward to verify the theoretical findings and to demonstrate the efficiency of the proposed scheme.
文献关键词：
中图分类号：
作者姓名：
Huan Liu;Xiangcheng Zheng;Hongfei Fu
作者机构：
School of Mathematical Sciences,Fadan University,Shanghai 200433,China;School of Mathematical Sciences,Peking University,Beijing 100871,China;School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China
文献出处：
引用格式：
[1]Huan Liu;Xiangcheng Zheng;Hongfei Fu-.ANALYSIS OF A MULTI-TERM VARIABLE-ORDER TIME-FRACTIONAL DIFFUSION EQUATION AND ITS GALERKIN FINITE ELEMENT APPROXIMATION)[J].计算数学（英文版）,2022(05):814-834
A类：
ANALYSIS,VARIABLE,FRACTIONAL,DIFFUSION,EQUATION,GALERKIN,FINITE,ELEMENT,APPROXIMATION
B类：
OF,MULTI,TERM,ORDER,TIME,AND,ITS,In,this,paper,study,well,posedness,solution,regularity,multi,term,variable,order,fractional,diffusion,equation,then,develop,optimal,Galerkin,finite,element,scheme,without,any,assumption,true,We,show,that,considered,problem,can,affected,by,maximum,value,initial,More,precisely,prove,belongs,C2,provided,has,integer,limit,near,data,sufficient,smoothness,otherwise,exhibits,same,singular,behavior,like,constant,counterpart,Based,these,results,convergence,Furthermore,efficient,parallel,algorithm,reduce,computational,costs,evaluation,derivatives,Numerical,experiments,are,forward,verify,theoretical,findings,demonstrate,efficiency,proposed
AB值：
0.511505
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