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\title{\large \bf The standard Galerkin and the streamline upwind finite element methods
for a priori chosen meshes; uniform \\ in $\varepsilon$ convergence in $L_2$-norm}
\author{\normalsize Owe Axelsson \\ \normalsize Department of Mathematics, University of Nijmegen\\
\normalsize 6525 ED Nijmegen, The Netherlands}
\date{}
\maketitle



\begin{abstract}
Uniform in $\varepsilon$ convergence of the discretization error in $L_2$-norm is
analysed for singularly perturbed convection diffusion problems using the standard
Galerkin and the streamline upwind finite element methods.

Thereby the dependence of the solution on the boundary layers and corner singularities is
taken into account. The analysis includes finite elements of arbitrary order. A certain
cancellation phenomenon is shown to hold for odd degree polynomials and quasiuniform
meshes, implying a rate of convergence close to optimal order.

The analysis is done for certain a priori determined meshes. Adaptively refined meshes
are also discussed. The numbers of mesh-points inside and outside the layer(s) are of
the same order, i.e.,  $O(h_0^{-2})$ in 2D, where $h_0$ is the coarse mesh parameter.

\end{abstract}

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