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In this study, we present a stabilized finite element analysis for completelyunified Stokes-Brinkman problems fully coupled with variable coefficienttransient Advection-Diffusion-Reaction equation(VADR). As well we have carriedout the stabilized finite element analysis for Stokes-Brinkman model withinterface conditions fully coupled with VADR. The viscosity of the fluid,involved in flow problem, depends on the concentration of the solute, whosetransport is described by VADR equation. The algebraic subgrid multiscaleapproach has been employed to arrive at the stabilized coupled variationalformulation. For the time discretization the fully implicit Euler scheme hasbeen used. A detailed derivation of both the apriori and aposteriori estimatesfor the stabilized subgrid multiscale finite element scheme have beenpresented. Few numerical experiments have been carried out to verify thecredibility of the method.

Apriori and aposteriori error estimation of Subgrid multiscale stabilized finite element method for coupled unified Stokes-Brinkman/Transport model