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A discontinuous finite difference streamline diffusion method for time-dependent hyperbolic problems

✍ Scribed by Yang Zhang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
604 KB
Volume
58
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this article, a new finite element method, discontinuous finite difference streamline diffusion method (DFDSD), is constructed and studied for first-order linear hyperbolic problems. This method combines the benefit of the discontinuous Galerkin method and the streamline diffusion finite element method. Two fully discrete DFDSD schemes (Euler DFDSD and Crank-Nicolson (CN) DFDSD) are constructed by making use of the difference discrete method for time variables and the discontinuous streamline diffusion method for space variables. The stability and optimal L 2 norm error estimates are established for the constructed schemes. This method makes contributions to the discontinuous methods. Finally, a numerical example is provided to show the benefit of high efficiency and simple implementation of the schemes.

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✍ Long Chen; Yonggang Wang; Jinbiao Wu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 195 KB

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