Fitted scheme of the finite element method for a convection-diffusion equation

Abstract

We consider the Galerkin piecewise linear finite element method for an ordinary convectiondiffusion boundary value problem with a small parameter in front of the highest derivative. For the generation of a discrete linear algebraic System we use the special quadrature formulae that take into account the boundary layer character of the solution. It is proved that the resulting discrete problem is of ε 2 + Λ 2 -Order of accuracy in the uniform discrete norm for small h and ε. The numerical example shows the advantage of the considered discrete scheine over two commonly used difference schemes.'Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk 660036, Russia

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