  We consider a filter stabilization technique with a deconvolution-based
indicator function for the simulation of advection dominated
advection-diffusion-reaction (ADR) problems with under-refined meshes. The
proposed technique has been previously applied to the incompressible
Navier-Stokes equations and has been successfully validated against
experimental data. However, it was found that some key parameters in this
approach have a strong impact on the solution. To better understand the role of
these parameters, we consider ADR problems, which are simpler than
incompressible flow problems. For the implementation of the filter
stabilization technique to ADR problems we adopt a three-step algorithm that
requires (i) the solution of the given problem on an under-refined mesh, (ii)
the application of a filter to the computed solution, and (iii) a relaxation
step. We compare our deconvolution-based approach to classical stabilization
methods and test its sensitivity to model parameters on a 2D benchmark problem.
