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Mathematical models that involve a combination of convective and diffusive processes are among the most widespread in all of science, engineering and other fields where mathematical modelling is important.Water quality problems, convective heat transfer problems, simulation of the semiconductor devices can be given as an example of these models. Also, the Linearization of the Navier-Stokes equation and drift-diffusion equation of semiconductor device modelling are important instances. The dimensionless parameter that measures the relative strenght of diffusion is generally quite small; so one often meets with situations where thin boundary and interior layers are present and singular perturbation problems arise. In this case,the main difficulty is to obtain a numerical solution which converges -Uniformly to the exact solution of the problem. In this work, the numerical approximations of the convection diffusion problem both on a uniform and non-uniform meshes are investigated. Also,it is shown that these numerical approximations have -Uniform convergency. This book will be useful for ones who research on this subject area.