A stabilized finite element method for convection–diffusion problems

A stabilized finite element method (FEM) is presented for solving the convection–diffusion equation. We enrich the linear finite element space with local functions chosen according to the guidelines of the residual‐free bubble (RFB) FEM. In our approach, the bubble part of the solution (the microscales) is approximated via an adequate choice of discontinuous bubbles allowing static condensation. This leads to a streamline‐diffusion FEM with an explicit formula for the stability parameter τ_K that incorporates the flow direction, has the capability to deal with problems where there is substantial variation of the Péclet number, and gives the same limit as the RFB method. The method produces the same a priori error estimates that are typically obtained with streamline‐upwind Petrov/Galerkin and RFB. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011