  In this paper, we describe a stable finite element formulation for
advection-diffusion-reaction problems that allows for robust automatic adaptive
strategies to be easily implemented. We consider locally vanishing,
heterogeneous, and anisotropic diffusivities, as well as advection-dominated
diffusion problems. The general stabilized finite element framework was
described and analyzed in arXiv:1907.12605v3 for linear problems in general,
and tested for pure advection problems. The method seeks for the discrete
solution through a residual minimization process on a proper stable
discontinuous Galerkin (dG) dual norm. This technique leads to a saddle-point
problem that delivers a stable discrete solution and a robust error estimate
that can drive mesh adaptivity. In this work, we demonstrate the efficiency of
the method in extreme scenarios, delivering stable solutions. The quality and
performance of the solutions are comparable to classical discontinuous Galerkin
formulations in the respective discrete space norm on each mesh. Meanwhile,
this technique allows us to solve on coarse meshes and adapt the solution to
achieve a user-specified solution quality.
