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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.
KeywordsSpectral Method Collocation Method Collocation Point Regularity Index Weighted Residual Method
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