Finite Difference Methods

In this notes, we summarize numerical methods for solving Stokes equations on rectangular grid, and solve it by multigrid vcycle method with distributive Gauss-Seidel relaxation as smoothing. The numerical methods we concerned are MAC scheme, nonconforming rotate bilinear FEM and nonconforming rotate bilinear FVM. 1. PROBLEM STATEMENT We consider Stokes equation (1.1) 8 >< >: μ ~ u + rp =~ f in ⌦, r · ~ u =0 in ⌦. ~ u =0 on @⌦ where ~ u = (u, v), and ~ f = (f1, f2). 2. MAC DISCRETIZATION