A globally divergence-free weak Galerkin finite element method with IMEX-SAV scheme for the Kelvin–Voigt viscoelastic fluid flow model with high Reynolds number

Abstract

In this manuscript, we present a globally divergence-free weak Galerkin finite element method with the IMEX-SAV scheme for solving the Kelvin–Voigt viscoelastic fluid flow model. Firstly, the weak Galerkin finite element method is used to analyze the spatial discretization, this method can yield globally divergence-free velocity solutions. Secondly, the IMEX-SAV difference scheme is adopted in the temporal discretization for the fully discrete scheme, and we can obtain the unconditional stability result for the velocity. In addition, combined with the stabilization idea, the method can not only reduce the spurious numerical oscillation at the high Reynolds number but also yield the uniform results that the constants in the error estimates do not explicitly depend on the inverse power of the physical parameters of the Kelvin–Voigt viscoelastic fluid flow model. Finally, several numerical experiments are performed to verify the theoretical results.