Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations

Abstract

This paper focuses on the time–space fractional convection–diffusion equations with time fractional derivative (of order $$\alpha $$ , $$0< \alpha <1$$ ) and space fractional derivative (of order $$\beta $$ , $$1<\beta <2$$ ). An approach based on a combination of local discontinuous Galerkin (in space) and finite difference methods (in time) is presented to solve the fractional convection–diffusion equations. The stability and convergence analysis of the method are given. Numerical results confirm the theory of the method for fractional convection–diffusion equations.