The time-fractional Oseen equations are studied in this article, where the time-fractional derivative is in the sense of Caputo of order \(\alpha \in (0,1)\) . The L1 formula with uniform and nonuniform meshes is applied to approximating the temporal fractional derivative, and the local discontinuous Galerkin method is developed to approach the space derivative. The numerical stability and the error estimates of the constructed schemes concerning velocity, stress (gradient of velocity), and pressure are shown. Moreover, the fast L1 algorithm is developed to accelerate the evaluation of the Caputo derivative. Finally, numerical examples are presented to testify the effectiveness of the derived algorithms.
Mathematics Subject Classification. 65M60, 35R11, 65M12.
