Aposteriori error estimation of Subgrid multiscale stabilized finite element method for transient Stokes model

In this study, we present a novel stabilized finite element analysis for transient Stokes model. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. Derivation of the stabilized form as well as stability analysis of it's fully discrete formulation are presented elaborately. Discrete $inf$-$sup$ condition for pressure stabilization has been proven. For the time discretization the fully implicit schemes have been used. A detailed derivation of the aposteriori error estimate for the stabilized subgrid multiscale finite element scheme has been presented. Numerical experiment has been carried out to verify theoretically established order of convergence.