(untitled) (Journal of Computational Mathematics, 2022)
Two nonconforming penalty methods for the two-dimensional stationary Navier-Stokes equations are studied in this paper. These methods are based on the weakly continuous P_1 vector fields and the locally divergence-free (LDF) finite elements, which respectively penalize local divergence and are discontinuous across edges. These methods have no penalty factors and avoid solving the saddle-point problems. The existence and uniqueness of the velocity solution are proved, and the optimal error estimates of the energy norms and L^2-norms are obtained. Moreover, we propose unified pressure recovery algorithms and prove the optimal error estimates of L^2-norm for pressure. We design a unified iterative method for numerical experiments to verify the correctness of the theoretical analysis.