On subgrid multiscale stabilized finite element method for advection-diffusion-reaction equation with variable coefficients

Abstract: 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.