We　consider　the　numerical　implementations　of　the　standard　one-level　finite　element　method　and　two-level　finite　element　method　for　the　steady　and　the　unsteady　Navier-Stokes　equations,　respectively.　Two　numerical　examples　are　presented:　first,　we　solve　the　steady　Navier-Stokes　equations　in　a　bounded　multiple　connected　domain　by　the　standard　one-level　finite　element　method,　while　we　calculate　the　unsteady　Navier-Stokes　equations　by　full　discrete　two-level　finite　element　method.　The　numerical　results　show　that　the　two　methods　are　feasible,　and　the　new　two-level　finite　element　method　is　significantly　effective.　(c)　2006　Elsevier　Inc.　All　rights　reserved.