  In this study a stabilized finite element method for solving
advection-diffusion-reaction equation with spatially variable coefficients has
been carried out. Here subgrid scale approach along with algebraic
approximation to the sub-scales has been chosen as stabilized method among
various other methods. Both a priori and a posteriori finite element error
estimates in $L_2$ norms have been derived after introducing the stabilized
formulation of the variational form. An expression of the stabilization
parameter for this 2D problem has also been derived here. At last numerical
experiments are presented to verify numerical performance of the stabilized
method and check the credibility of the theoretically derived expression of the
stabilization parameter.
