α-robust analysis of the mixed finite element method for the time-fractional Navier-Stokes equations

Abstract This study investigates the fully discrete mixed finite element approximation for the Navier-Stokes equations,incorporating the Caputo fractional derivative with an order α∈(0,1).For spatial discretization of the time-fractional Navier-Stokes equations,the Taylor-Hood finite element method is utilized.In the temporal direction, both the L1 scheme and the fast L1 scheme are employed under nonuniform meshes.The stability and convergence of these schemes are established,evaluating the velocity field in both L²-norm and H¹-norm,and the pressure in the L²-norm. Notably, all results demonstrate α-robustness,ensuring their validity as α approaches 1 from the left.Furthermore, numerical experiments are conducted to validate the theoretical findings,and comparisons with the classical Navier-Stokes equations are presentedto enhance comprehension and practical application of these two model types. Mathematics Subject Classification. 65M06; 65M12; 65M60.