We semi-discretize in space a time-dependent Navier-Stokes systemon a three-dimensional polyhedron by finite-elements schemesdefined on two grids. In the first step, the fully non-linearproblem is semi-discretized on a coarse grid, with mesh-size H.In the second step, the problem is linearized by substitutinginto the non-linear term, the velocity u H computed at stepone, and the linearized problem is semi-discretized on a finegrid with mesh-size h. This approach is motivated by the factthat, on a convex polyhedron and under adequate assumptions on thedata, the contribution of u H to the error analysis ismeasured in the L 2 norm in space and time, and thus, for thelowest-degree elements, is of the order of H 2. Hence, an errorof the order of h can be recovered at the second step, providedh = H 2.
