A note on the finite element method for the space-fractional advection diffusion equation

Computers and Mathematics with Applications

Volumn 59, Issue 5, 2010, Pages 1718-1726

  Zheng, Yunying ^a,b   Li, Changpin ^a   Zhao, Zhengang ^a  

^a SHANGHAI UNIVERSITY   (China)

^b HUAINAN NORMAL UNIVERSITY   (China)

Author keywords

Caputo derivative; Finite element method; Space fractional partial differential equation

Indexed keywords

ADVECTION DIFFUSION EQUATION; CAPUTO DERIVATIVE; CAPUTO DERIVATIVES; ERROR ESTIMATES; FRACTIONAL DERIVATIVES; NON-HOMOGENEOUS; NUMERICAL RESULTS; THEORETICAL RESULT;

ADVECTION; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; COMPUTATIONAL FLUID DYNAMICS; PARTIAL DIFFERENTIAL EQUATIONS;

FINITE ELEMENT METHOD;

EID: 76449122108     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.08.071     Document Type: Article

References (14)

1. Deng W.H., and Li C.P. The evolution of chaotic dynamics for fractional unified system. Phys. Lett. A 372 (2008) 401-407
2. Li C.P., and Peng G.J. Chaos in Chen's system with a fractional order. Chaos Solitons Fractals 22 2 (2004) 443-450
3. Li C.P., and Deng W.H. Remark on fractional derivatives. Appl. Math. Comput. 187 (2007) 777-784
4. Heymans N., and Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheol. Acta. 45 (2006) 765-772
5. Biler P., and Woyczynski W.A. Global and exploding solutions for nonlocal quadratic evolution problems. SIAM J. Appl. Math. 59 (1998) 845-869
6. Bergh J., and Löfström J. Interpolation Spaces, An Introduction (1976), Springer-Verlag, New York, Berlin
7. 2. J. Comput. Appl. Math. 193 (2006) 243-268
8. Fix G.J., and Roop J.P. Least square Finite-element solution of a fractional order two-point boundary value problem. Comput. Math. Appl. 48 (2004) 1017-1033
9. Ervin V.J., and Roop J.P. Variational formulation for the stationary fractional advection dispersion equation. Numer. Methods Partial Differential Equations 22 (2006) 558-576
10. Adams R.A. Sobolev Spaces (1975), Academic Press
11. Brenner S.C., and Scott L.R. The Mathematical Theory of Finite Element Methods (1994), Springer-Verlag, New York, Berlin
12. Heywood J.G., and Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problem, Part IV: Error analysis for second-order time discretization. SIAM J. Numer. Anal. 2 (1990) 353-384
13. Chen J.H., and Liu F. Analysis of stability and convergence of numerical approximation for the Riesz fractional reaction-dispersion equation. J. Xiamen Univ. (Natural Science) 45 4 (2006) 465-469
14. Ray S.S., Chaudhuri K.S., and Bera R.K. Application of modified decomposition method for the analytical solution of space fractional diffusion equation. Appl. Math. Comput. 196 (2008) 294-302