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

摘要

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