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

摘要

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~∞ (L~2)-norm and L~∞ (H~1)-norm for velocity and L~∞ (L~2)-norm for pressure are established. These estimates are shown to be uniform in time. Numerical results are provided to verify the theoretical estimates.