Linear Conforming and Nonconforming Upwind Finite Elements for the Convection-Diffusion Equation

A conforming and a nonconforming method for the approximationof the stationary 2-D convection-diffusion equation at highP?clet number are presented. Convergence of order h is provedin a generic case and, for a particular choice of the upwindschemes, a discrete maximum principle is established under veryunrestrictive conditions on the mesh. Results of numerical computationsare produced to show the practical convergence of these methods.