Moving finite element methods for time fractional partial differential equations

With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and...

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Bibliographic Details
Published inScience China. Mathematics Vol. 56; no. 6; pp. 1287 - 1300
Main Authors Jiang, YingJun, Ma, JingTang
Format Journal Article
LanguageEnglish
Published Heidelberg SP Science China Press 01.06.2013
Subjects
Applications of Mathematics
China
Computer simulation
Convergence
Derivatives
Finite element method
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Partial differential equations
偏微分方程
分数阶
和空间
时间导数
有限元方法
爆破解
移动
线性时间
65R20
65M06
35S10
fractional partial differential equations
65M60
moving finite element methods
blow-up solutions
65M12
Online AccessGet full text
ISSN1674-7283
1869-1862
DOI10.1007/s11425-013-4584-2

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Summary:With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.
Bibliography:fractional partial differential equations, moving finite element methods, blow-up solutions
With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-013-4584-2