An adaptive stabilized finite element scheme for the advection-reaction-diffusion equation

An adaptive finite element scheme for the advection-reaction-diffusion equation is introduced and analyzed. This scheme is based on a stabilized finite element method combined with a residual error estimator. The estimator is proved to be reliable and efficient. More precisely, global upper and local lower error estimates with constants depending at most on the local mesh Peclet number are proved. The effectiveness of this approach is illustrated by several numerical experiments.