This　survey　enfolds　rigorous　analysis　of　the　defect-correction　finite　element　(FE)　method　for　the　time-dependent　conduction-convection　problem　which　based　on　the　Crank-Nicolson　scheme.　The　method　consists　of　two　steps:　solve　a　nonlinear　problem　with　an　added　artificial　viscosity　term　on　a　FE　grid　and　correct　the　solutions　on　the　same　grid　using　a　linearized　defect-correction　technique.　The　stability　and　optimal　error　estimate　of　the　fully　discrete　scheme　are　derived.　As　a　consequence,　the　effectiveness　of　the　method　to　deal　with　high　Reynolds　number　is　illustrated　in　several　numerical　experiments.　(c)　2016　Wiley　Periodicals,　Inc.　Numer　Methods　Partial　Differential　Eq　33:　681-703,　2017