Non-uniform L۱/DG method for one-dimensional time-fractional convection equation

In this paper, we present an efficient 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 the order in (۰, ۱) is discretized by the L۱ finite difference method on non-uniform meshes and the spatial derivative by the discontinuous Galerkin (DG) finite element method. The stability and convergence of the method are analyzed. Numerical experiments are provided to confirm the theoretical results.

Keywords:

time-fractional convection equation , L۱ scheme , discontinuous Galerkin method , stability and convergence