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 VhVh be the linear finite element space on a suitable grid ThTh. A variant of streamline diffusion finite element method is proved to be almost uniform stable in the sense that the numerical approximation uhuh satisfies ∥u-uh∥∞⩽C|lnε|∥u-uh∥∞⩽C|lnε|infvh∈Vh∥u-vh∥∞,infvh∈Vh∥u-vh∥∞, where C   is independent with the small diffusion coefficient εε and the mesh ThTh. Such stability result is applied to layer-adapted grids to obtain almost εε-uniform second order scheme for turning point problems.