The finite element method on adapted meshes for the two-dimensional convection diffusion problem

We consider a singularly perturbed elliptic boundary value problem which models a special channel flow. Basing on the decomposition of the exact solution we obtain a priori bounds for derivatives of the exact solution. For the numerical solution, we used linear finite elements on an adapted meshes, further we discuss the additive extraction method. We obtain uniform estimates for the approximate solution in some energetic norm.