Stability and convergence of a fully discrete local discontinuous Galerkin method for multi-term time fractional diffusion equations.

In this paper, a fully discrete local discontinuous Galerkin method for a class of multi-term time fractional diffusion equations is proposed and analyzed. Using local discontinuous Galerkin method in spatial direction and classical L1 approximation in temporal direction, a fully discrete scheme is established. By choosing the numerical flux carefully, we prove that the method is unconditionally stable and convergent with order O( h + (Δ t)), where k, h, and Δ t are the degree of piecewise polynomial, the space, and time step sizes, respectively. Numerical examples are carried out to illustrate the effectiveness of the numerical scheme. [ABSTRACT FROM AUTHOR]