Analysis of divergence-free h-1 conforming fem with imex-sav scheme for the navier-stokes equations at high reynolds number

In this paper, we analyze the first-order implicit-explicit type scheme based on the scalar auxiliary variable (SAV) with divergence-free H-1 conforming finite element method (FEM) in space for the evolutionary incompressible Navier-Stokes equations at high Reynolds number. The stability and a priori error estimates are given, in which the constants are independent of the Reynolds number. The velocity energy estimate is given without any condition on the time step, however, the a priori error estimates for the velocity are obtained with severe time step restrictions. In addition, a Reynolds-dependent error bound with convergence order of k + 1 in space is also obtained for the velocity error in the L-2 norm with no time step restrictions. Here, k is the polynomial order of the velocity space. Some numerical experiments are carried out to verify the analytical results.