A Finite Element Formulation for the Numerical Solution of the Convection – Diffusion Equation

In this work we present several finite element techniques to solve the convection-diffusion equation when the Péclet number is high, that is, when diffusion is very small. The problem in this case becomes a singularly perturbed one, since its nature changes when the zero diffusion case is considered. Physically, this is reflected by the appearence of very narrow zones with steep gradients of the solution, either to accomodate the boundary conditions (boundary layers) or to advect discontinuous profiles into the computational domain (internal layers).