  In this study, a stabilized finite element analysis of unified
Stokes-Darcy-Brinkman system fully coupled with variable coefficient
Advection-Diffusion-Reaction equation(VADR) has been carried out. The viscosity
of the fluid, involved in Stokes-Darcy flow, depends on the concentration of
the solute, whose transport is described by VADR equation. The algebraic
subgrid multiscale approach has been employed to arrive at the stabilized
coupled variational formulation. For the time discretization the fully implicit
Euler scheme has been used. A detailed derivation of both the apriori and
aposteriori estimates for the stabilized subgrid multiscale finite element
scheme have been presented. Few numerical experiments have been carried out to
verify the credibility of the method.
