A comparison of three kinds of local and parallel finite element algorithms based on two-grid discretizations for the stationary Navier–Stokes equations

Based on two-grid discretizations, three kinds of local and parallel finite element algorithms for the stationary Navier–Stokes equations are introduced and discussed. The main technique is first to use a standard finite element discretization on a coarse grid to approximate low frequencies of the solution, then to apply some linearized discretizations on a fine grid to correct the resulted residual (which contains mostly high frequencies) by some local and parallel procedures. Three approaches to linearization are discussed. Under the uniqueness condition, error estimates of the finite element solution are derived. Numerical results show that among the three kinds of parallel algorithms, the Oseen-linearized algorithm is preferable if we both consider the computational time and the accuracy of the approximate solution.