Spectral methods for hyperbolic problems

By David I. Gottlieb, Jan S. Hesthaven. 2001

332 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/093c2a19e5c6d6382a7fa85bb8e7fdc53f1a9797

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In Computational Mechanics

In Mathematical Physics

Citations in the corpus

Local spectral time splitting method for first- and second-order partial differential equations (2005, unknown): “: +1 517 353 4689. ail address: wei@math.msu.edu (G.W. Wei).”
Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon (2004, methodology): “The most popular algorithm relies on 2ltering out the high-frequency components and considerably reducing the over or undershoots near the discontinuities [3,10].”
Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations (2005, background): “The success of Gegenbauer reconstruction has spawned an industry of theoretical papers [21,16–19,12,9,10,23–25,32,26,11] and applications in fluid mechanics [29–31,7], hyperbolic waves [15], local Fourier methods [35,36] and medical imaging [2,1,3,14].”
A pseudospectral method of solution of Fisher's equation (2006, methodology): “methods have also been used for the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations [22].”
A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations (2015, methodology): “Spectral methods (see, for instance [1–6]) are one of the principal methods of discretization for the numerical solution of differential equations.”
SPECTRAL METHODS FOR TIME-DEPENDENT PROBLEMS. (2007, methodology): “The more direct use of filters for stabilization as discussed here was introduced in Gottlieb and Hesthaven (2001).”
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations (2002, background): “As has been shown over the last decade, such filtering can be applied without sacrificing spectral accuracy [12, 28].”