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

In this study a stabilized finite element method for solving advection-diffusion-reaction equation with spatially variable coefficients has been introduced. Here subgrid scale approach along with algebraic approximation to the sub-scales has been chosen to stabilize the Galerkin finite element method. Both a priori and a posteriori finite element error estimates in L-2 norm have been derived after introducing the stabilized variational form. An expression of the stabilization parameter has also been derived here. At last numerical experiments are presented to verify numerical performance of the stabilized method and the credibility of the theoretically derived expression of the stabilization parameter has been established numerically. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.