Volume 32, pp. 63-75, 2008.

A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation

Hans-Görg Roos and Reiner Vanselow

Abstract

Some recently developed finite element stabilizations of convection-diffusion problems generate in 1D five-point difference schemes. Because there are only few results on four- and five-point schemes in the literature (in contrast to three-point schemes), we discuss some properties of such schemes with special emphasis on the choice of free parameters for a singularly perturbed problem to avoid oscillations.

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Key words

convection-diffusion, difference scheme, stabilized finite element method

AMS subject classifications

65L10, 65L12, 65L60

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