Abstract
In this study, an efficient approach for solving the two-dimensional time-fractional convection problem with a non-smooth solution in the temporal direction is proposed. The solution exhibits weakly regular at the initial time, so the L1 formula on the nonuniform meshes is applied to discretizing the Caputo derivative. In the spatial direction, the central discontinuous Galerkin (CDG) method involving two approximate solutions defined on overlapping elements is used. The fully discrete scheme is proven to be numerically stable, and the optimal convergence result is attained. A few numerical experiments are conducted to confirm the theoretical conclusions.
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