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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Introduction
verfasst von : Jie Shen, Tao Tang, Li-Lian Wang
Erschienen in: Spectral Methods
Verlag: Springer Berlin Heidelberg
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Numerical methods for partial differential equations can be classified into the local and global categories. The finite-difference and finite-element methods are based on local arguments, whereas the spectral method is global in character. In practice, finite-element methods are particularly well suited to problems in complex geome-tries, whereas spectral methods can provide superior accuracy, at the expense of domain flexibility. We emphasize that there are many numerical approaches, such as hp finite-elements and spectral-elements, which combine advantages of both the global and local methods. However in this book, we shall restrict our attentions to the global spectral methods.