A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain. (15th April 2013)

• Record Type: Journal Article
• Authors: Zhao, Jingjun; Xiao, Jingyu; Xu, Yang
• Other Names: Hao Xinan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-04-15
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/868035
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We present an effective finite element method (FEM) for the multiterm time-space Riesz fractional advection-diffusion equations (MT-TS-RFADEs). We obtain the weak formulation of MT-TS-RFADEs and prove the existence and uniqueness of weak solution by the Lax-Milgram theorem. For multiterm time discretization, we use the Diethelm fractional backward finite difference method based on quadrature. For spatial discretization, we show the details of an FEM for such MT-TS-RFADEs. Then, stability and convergence of such numerical method are proved, and some numerical examples are given to match well with the main conclusions.