Titlebook: Implementing Spectral Methods for Partial Differential Equations; Algorithms for Scien David A. Kopriva Book 2009 Springer Science+Business

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Algorithms for Non-Periodic Functionse the Legendre and Chebyshev polynomials themselves. Those algorithms are then used to compute the Gauss quadrature nodes and weights that are needed in turn to compute interpolants and discrete inner products. The chapter ends with algorithms used to approximate the derivatives that appear in PDEs

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Survey of Spectral ApproximationsThe methods developed are the Fourier collocation and Galerkin methods, polynomial collocation and Galerkin methods, and nodal continuous and discontinuous Galerkin methods. At the end of the chapter, after it is clear what the methods are, how they are derived, and how they are implemented, a discu

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Spectral Methods in Non-Square Geometriesoblems on quadrilateral domains. Benchmark solutions include potentials in non-square domains, incompressible flow over a circular obstacle, potential in an annulus, advection-diffusion in curved channels, and acoustic scattering off a cylinder.

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Spectral Element Methodsn spectral methods, and spectral element methods in particular, the domain of interest is subdivided into smaller subdomains that are mapped individually onto the square, allowing problems in truly complex geometries to be solved. Spectral element methods are introduced for one space dimension then

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978-90-481-8484-2Springer Science+Business Media B.V. 2009