Convergence analysis of a LDG method for tempered fractional convection–diffusion equations

Abstract

This paper proposes a local discontinuous Galerkin method for tempered fractional convection–diffusion equations. The tempered fractional convection–diffusion is converted to a system of the first order of differential/integral equation, then, the local discontinuous Galerkin method is employed to solve the system. The stability and order of convergence of the method are proven. The order of convergence O(hk+1) depends on the choice of numerical fluxes. The provided numerical examples confirm the analysis of the numerical scheme.