Study of local refinements in numerical methods for advection-diffusion equations

In the context of advection diffusion problems, we consider scalar convection-diffusion problems in 2-D. We try to obtain an adaptive grid refinement of every original defined domain. This refinement should be well localized at the so called "boundary layers". For this proposal we use three kind of a posteriori errors estimators. They are based on the evaluation of local residual, on the solution of discrete local Neumann problems and on the gradient recovery. We investigate efficiency and the good qualities of these estimators, by some benchmarks, highlighting advantages and disadvantages for every one of them. In all our tests we use piecewise linear polynomials and SUPG method with Galerkin projection method.