A posteriori error analysis of time-dependent Stokes problem by Chorin-Temam scheme

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We present a posteriori-residual analysis for the approximate time-dependent Stokes model Chorin-Temam projection scheme (Chorin in Math. Comput. 23:341---353, 1969; Temam in Arch. Ration. Mech. Appl. 33:377---385, 1969). Based on the multi-step approach introduced in Bergam et al. (Math. Comput. 74(251):1117---1138, 2004), we derive error estimators, with respect to both time and space approximations, related to diffusive and incompressible parts of Stokes equations. Using a conforming finite element discretization, we prove the equivalence between error and estimators under specific conditions.