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A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain. (English) Zbl 1275.65064

Summary: 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 solutions 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.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
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