Analysis of a fully discrete local discontinuous Galerkin method for time-fractional fourth-order problems

被引：94

作者：

Wei, Leilei ^{[1
,2
]}

He, Yinnian ^{[2
]}

机构：

[1] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Henan, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Time-fractional partial differential equations; Fourth-order problems; Local discontinuous Galerkin method; Stability; Error estimates; ANOMALOUS SUBDIFFUSION EQUATION; PARTIAL-DIFFERENTIAL-EQUATIONS; HOMOTOPY PERTURBATION METHOD; DIFFUSION EQUATION; SPACE; DERIVATIVES; STABILITY; SYSTEMS;

D O I：

10.1016/j.apm.2013.07.040

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we propose and analyze a fully discrete local discontinuous Galerkin (LOG) finite element method for time-fractional fourth-order problems. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Stability is ensured by a careful choice of interface numerical fluxes. We prove that our scheme is unconditional stable and convergent. Numerical examples are shown to illustrate the efficiency and accuracy of our scheme. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1511 / 1522

页数：12

共 32 条

[1] Generalized variational calculus in terms of multi-parameters fractional derivatives [J].

Agrawal, Om P. ;

Muslih, Sami I. ;

Baleanu, Dumitru .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (12) :4756-4767

[2] A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives [J].

Baleanu, Dumitru ;

Trujillo, Juan I. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (05) :1111-1115

[3] Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation [J].

Chen, Chang-ming ;

Liu, F. ;

Burrage, K. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 198 (02) :754-769

[4] The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J].

Cockburn, B ;

Shu, CW .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (06) :2440-2463

[5] Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids [J].

Cockburn, B ;

Kanschat, G ;

Perugia, I ;

Schötzau, D .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2001, 39 (01) :264-285

[6] FINITE ELEMENT METHOD FOR THE SPACE AND TIME FRACTIONAL FOKKER-PLANCK EQUATION [J].

Deng, Weihua .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 47 (01) :204-226

[7] Least squares finite-element solution of a fractional order two-point boundary value problem [J].

Fix, GJ ;

Roop, JP .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2004, 48 (7-8) :1017-1033

[8]

Gu YT, 2010, CMES-COMP MODEL ENG, V56, P303

[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] Finite difference/spectral approximations for the time-fractional diffusion equation [J].

Lin, Yumin ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (02) :1533-1552

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