A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain

作者：Zhao, Jingjun; Xiao, Jingyu; Xu, Yang^*

来源：Abstract and Applied Analysis, 2013, 2013: 868035.

DOI：10.1155/2013/868035

• DIFFERENTIAL-EQUATIONS
• NUMERICAL APPROXIMATION
• ADAPTIVE DISCRETIZATION
• DISPERSION EQUATIONS
• BOUNDED DOMAINS
• SPECTRAL METHOD

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.

• 出版日期2013
• 单位哈尔滨工业大学