Non-uniform L1/DG method for one-dimensional time-fractional convection equation

In this paper, we present an effcient numerical method to solve a one-dimensional time-fractional convection equation whose solution has a certain weak regularity at the starting time, where the time-fractional derivative in the Caputo sense with order in (0; 1) is discretized by the L1 nite difference method on non-uniform meshes and the spatial derivative by the discontinuous Galerkin (DG) nite element method. The stability and convergence of the method are analyzed. Numerical experiments are provided to coniform the theoretical results.