| Abstract: | We consider streamline diffusion finite element methods applied to a singularly perturbed convection–diffusion two‐point boundary
value problem whose solution has a single boundary layer. To analyse the convergence of these methods, we rewrite them as
finite difference schemes. We first consider arbitrary meshes, then, in analysing the scheme on a Shishkin mesh, we consider
two formulations on the fine part of the mesh: the usual streamline diffusion upwinding and the standard Galerkin method.
The error estimates are given in the discrete L
∞ norm; in particular we give the first analysis that shows precisely how the error depends on the user-chosen parameter τ0 specifying the mesh. When τ0 is too small, the error becomes O(1), but for τ0 above a certain threshold value, the error is small and increases either linearly or quadratically as a function of . Numerical
tests support our theoretical results.
This revised version was published online in August 2006 with corrections to the Cover Date. |
