Convergence analysis of moving finite element methods for space fractional differential equations

被引：42
|
作者：
Ma, Jingtang [1 ]
Liu, Jinqiang [2 ]
Zhou, Zhiqiang [3 ]
机构：
[1] Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 611130, Peoples R China
[2] Southwestern Univ Finance & Econ, Sch Finance, Chengdu 611130, Peoples R China
[3] Huaihua Univ, Dept Math, Huaihua 418008, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 255卷
基金：
中国国家自然科学基金;
关键词：
Finite element methods; Fractional differential equations; Convergence analysis; ADVECTION-DISPERSION EQUATION; NEUMANN BOUNDARY-CONDITIONS; SUB-DIFFUSION EQUATIONS; NUMERICAL APPROXIMATION; SUBDIFFUSION EQUATION; GALERKIN METHODS; SCHEME; MESH;
D O I：
10.1016/j.cam.2013.06.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Most existent papers have focused on the fixed mesh methods for solving space fractional differential equations. However since some classes of space fractional differential equations may have singular or even finite-time blowup solutions, it is highly needed to develop adaptive mesh methods to solve these problems. In this paper the moving finite element methods are studied for a class of time-dependent space fractional differential equations. The convergence theories of the methods are derived with L-2-norm and numerical examples are provided to support the theoretical results. To simplify the analysis, a fractional Ritz projection operator is introduced and the error estimation of the projection is derived under the moving mesh setting. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：661 / 670
页数：10
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