Stability and Error Estimates of Galerkin Finite Element Approximations for Convection—Diffusion Equations

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Abstract
The stability of finite element approximations of convection (or advection) dominated diffusion equations is considered. We show that if we apply an exponentially decreasing weight in the layer elements, the classical Galerkin approximation is stable uniformly with respect to the ratio of diffusion and convection coefficients. Hence no “upwinding” is needed other than in the layer elements. This result includes some turning point problems.

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