Modified marker and cell schemes for Stokes equations with Dirichlet boundary condition.

In this paper, we proposed a modified marker and cell (MMAC) method for solving the steady‐state Stokes equations with Dirichlet boundary condition. We reconstruct the marker and cell (MAC) schemes by using the quadratic Lagrange extrapolation method to approximate the value of ghost points near the boundary. First, we prove the stability of the proposed scheme rigorously. Then, we obtain the second‐order superconvergence for pressure in the discrete L2$$ {L}^2 $$ norm and velocity in the discrete H1$$ {H}^1 $$ norm by constructing auxiliary functions and discretizing parameters. Meanwhile, we present two MMAC schemes for the time‐dependent Stokes equations by a similar method. Finally, we provide some numerical experiments to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]