In this paper, we apply a two-grid scheme to the DG formulation of the 2D transient Navier–Stokes model.
The two-grid algorithm consists of the following steps: Step 1 involves solving the nonlinear system on a coarse mesh with mesh size 𝐻, and Step 2 involves linearizing the nonlinear system by using the coarse grid solution on a fine mesh of mesh size ℎ and solving the resulting system to produce an approximate solution with desired accuracy.
We establish optimal error estimates of the two-grid DG approximations for the velocity and pressure in energy and
L
2
L^{2}
-norms, respectively, for an appropriate choice of coarse and fine mesh parameters.
We further discretize the two-grid DG model in time, using the backward Euler method, and derive the fully discrete error estimates.
Finally, numerical results are presented to confirm the efficiency of the proposed scheme.