Numerical analysis for Navier-Stokes equations with time fractional derivatives

In this article, we study numerical approximation for a class of Navier-Stokes equations with time fractional derivatives. We propose a scheme using finite difference approach in fractional derivative and Legendre-spectral method approximations in space and prove that the scheme is unconditionally stable. In addition, the error estimate shows that the numerical solutions converge with the order O(Δt2−α+Δt−αN1−s), 0 < α < 1 being the order of the fractional derivative in time. Numerical examples are illustrated to verify the theoretical results.