A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain
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.
multiterm time-space Riesz fractional advection-diffusion equations
Diethelm fractional backward finite difference method
scientific article; zbMATH DE number 6209480
scientific article