Nonsmooth data error estimates for FEM approximations of the time fractional cable equation

被引：13

作者：

Zhu, Peng ^{[1
]}

Xie, Shenglan ^{[2
]}

Wang, Xiaoshen ^{[3
]}

机构：

[1] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Zhejiang, Peoples R China

[2] Jiaxing Univ, Nanhu Coll, Jiaxing 314001, Zhejiang, Peoples R China

[3] Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA

来源：

APPLIED NUMERICAL MATHEMATICS | 2017年 / 121卷

关键词：

Fractional cable equation; Convolution quadrature; Finite element method; Riemann-Liouville fractional derivative; Nonsmooth data error estimate; DIFFUSION-WAVE EQUATIONS; ANOMALOUS ELECTRODIFFUSION; CONVOLUTION QUADRATURE; DOMAIN SOLUTIONS; SCHEMES; MODELS;

D O I：

10.1016/j.apnum.2017.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the fractional cable equation, involving two Riemann-Liouville fractional derivatives, with initial/boundary condition is considered. Two fully discrete schemes are obtained by employing piecewise linear Galerkin FEM in space, and using convolution quadrature methods based on the first- and second-order backward difference methods in time. Optimal error estimates in terms of the initial data and the inhomogeneity for the semi-discrete scheme and fully discrete schemes are discussed. Numerical results are shown to verify the theoretical results. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：170 / 184

页数：15

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