Numerical methods for time-dependent convection-diffusion equations

We examine a singularly perturbed linear parabolic initial-boundary value problem in one space variable. Various finite difference schemes are derived for this problem using a semidiscrete Petrov—Galerkin finite element method. These schemes do not have a cell Reynolds number restriction and are shown to be first-order accurate, uniformly in the perturbation parameter. Numerical results are also presented.