Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.

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