Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in R 2 with L 2 Initial Data.

In this paper, we study the finite element method of the Navier–Stokes equations with the initial data belonging to the L 2 space for all time t > 0 . Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the H 1 -norm, when t ∈ [ 0 , 1) . Under the uniqueness condition, by applying the integral technique and the estimates in the negative norm, we deduce the uniform-in-time optimal error bounds for the velocity in H 1 -norm and the pressure in L 2 -norm. [ABSTRACT FROM AUTHOR]