A defect correction weak Galerkin finite element method for the Kelvin–Voigt viscoelastic fluid flow model

Abstract

In this paper, we present a defect correction weak Galerkin finite element method for solving the Kelvin–Voigt viscoelastic fluid flow model, which can guarantee that the discrete velocity is globally divergence-free. The second-order Crank–Nicolson difference scheme is considered for temporal discretization. In particular, combined with the defect correction method, the numerical oscillation effect is reduced at high Reynolds number. Our algorithm not only gives the stability and convergence of the numerical solutions of velocity and pressure but also is uniformly valid at the retardation time κ→0. Several numerical experiments are performed to verify the method has good behaviors.