On a two-grid finite element scheme combined with Crank–Nicolson method for the equations of motion arising in the Kelvin–Voigt model

In this paper, we present a second order accurate Crank–Nicolson scheme applied to a system arising from Galerkin finite element two-grid approximations to the equations of motion described by the Kelvin–Voigt viscoelastic fluid flow model. Optimal error estimates in L∞(L2)-norm and L∞(H1)-norm for velocity and L∞(L2)L∞(L2)-norm for pressure are established. These estimates are shown to be uniform in time. Numerical results are provided to verify the theoretical estimates.