# Stabilized subgrid multiscale finite element formulation for advection-diffusion-reaction equation with variable coefficients coupled with Stokes-Darcy equation

## TL;DR

This paper develops a stabilized finite element method for coupled advection-diffusion-reaction and Stokes-Darcy flow equations with variable coefficients, including error analysis and algebraic stabilization parameter approximation.

## Contribution

It introduces a novel stabilized finite element formulation for coupled ADR and Stokes-Darcy equations with algebraic stabilization parameter approximation.

## Key findings

- Effective stabilization of coupled equations demonstrated
- Error estimates provided for the proposed method
- Applicable to variable coefficient problems

## Abstract

In this paper subgrid multiscale stabilized finite element method for Advection-Diffusion-Reaction (ADR) equation coupled with Stokes-Darcy flow problem has been studied. Here the advection velocity involved in ADR equation obeys Stokes-Darcy flow equation. In this study the approach of algebraic approximation of stabilization parameter has been considered. Further apriori error estimation has been elaborately carried out.