Article ID Journal Published Year Pages File Type
4641965 Journal of Computational and Applied Mathematics 2008 13 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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