Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods
نویسندگان
چکیده
منابع مشابه
Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods
A general framework is introduced to analyze the approximation properties of mapped Legendre polynomials and of interpolations based on mapped Legendre–Gauss–Lobatto points. Optimal error estimates featuring explicit expressions on the mapping parameters for several popular mappings are derived. These results not only play an important role in numerical analysis of mapped Legendre spectral and ...
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Standard spectral methods are capable of providing very accurate approximations to well-behaved smooth functions with significantly less degrees of freedom when compared with finite difference or finite element methods (cf. [6,7,11]). However, if a function exhibits localized behaviors such as sharp interfaces, very thin internal or boundary layers, using a standard Gauss-type grid usually fail...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2004
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142903422065