Uniform in ε convergence of the standard Galerkin finite element method in L2-norm for the singularly-perturbed elliptic problems on a priori chosen meshes

Convection-diffusion problems are models for describing the transportation of matters in a diffusive medium. They are also a part of more general equations, such as the Navier-Stokes equations appearing in fluid flow problems. We consider the linear convection-diffusion problem of the special form and show that under the corresponding conditions it has a unique solution in the first order Sobolev space.