Finite elements for time-dependent convection-diffusion problems

This thesis analyses and makes comparison (both theoretical and practical) between a number of numerical methods based on finite elements for solving stationary and time-dependent initial and boundary value problems governed by linear, scalar convection-dominated convection-diffusion equations. We set about achieving our objective by analysing the stability properties of the methods, deriving discretion error estimates and qualitatively assessing the computational complexity of implementing the methods. A number of test problems are presented and solved; the numerical results are discussed, and some specific conclusions are drawn in a concluding chapter.