Moving finite element methods for time fractional partial differential equations

被引：42

作者：

Jiang YingJun ^{[1
]}

Ma JingTang ^{[2
]}

机构：

[1] Changsha Univ Sci & Technol, Dept Math & Sci Comp, Changsha 410076, Hunan, Peoples R China

[2] Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 611130, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 06期

基金：

中国国家自然科学基金;

关键词：

fractional partial differential equations; moving finite element methods; blow-up solutions; IMPLICIT NUMERICAL-METHOD; ERROR ANALYSIS; DIFFUSION;

D O I：

10.1007/s11425-013-4584-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuniform 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 - alpha for time and r for space are proved when the method is used for the linear time FPDEs with alpha-th order time derivatives. Numerical examples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.

引用

页码：1287 / 1300

页数：14

共 22 条

[1]

[Anonymous], 2002, TEXTS APPL MATH

[2] A Fourier method for the fractional diffusion equation describing sub-diffusion [J].

Chen, Chang-Ming ;

Liu, F. ;

Turner, I. ;

Anh, V. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 227 (02) :886-897

[3] Detailed error analysis for a fractional Adams method [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NUMERICAL ALGORITHMS, 2004, 36 (01) :31-52

[4] A predictor-corrector approach for the numerical solution of fractional differential equations [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :3-22

[5] Some recent advances in theory and simulation of fractional diffusion processes [J].

Gorenflo, Rudolf ;

Mainardi, Francesco .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 229 (02) :400-415

[6]

Huang WZ, 2011, APPL MATH SCI, V174, P1, DOI 10.1007/978-1-4419-7916-2

[7] MOVING MESH PARTIAL-DIFFERENTIAL EQUATIONS (MMPDES) BASED ON THE EQUIDISTRIBUTION PRINCIPLE [J].

HUANG, WZ ;

REN, YH ;

RUSSELL, RD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (03) :709-730

[8] Variational mesh adaptation II: error estimates and monitor functions [J].

Huang, WZ ;

Sun, WW .

JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 184 (02) :619-648

[9] High-order finite element methods for time-fractional partial differential equations [J].

Jiang, Yingjun ;

Ma, Jingtang .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (11) :3285-3290

[10] Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives [J].

Kirane, M ;

Laskri, Y ;

Tatar, NE .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 312 (02) :488-501

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