Stability of a streamline diffusion finite element method for turning point problems

A one-dimensional singularly perturbed problem with a boundary turning point is considered in this paper. Let V h be the linear finite element space on a suitable grid T h . A variant of streamline diffusion finite element method is proved to be almost uniform stable in the sense that the numerical approximation u h satisfies ∥ u - u h ∥ ∞ ⩽ C | ln ε | inf v h ∈ V h ∥ u - v h ∥ ∞ , where C is independent with the small diffusion coefficient ε and the mesh T h . Such stability result is applied to layer-adapted grids to obtain almost ε -uniform second order scheme for turning point problems.