SPECTRAL METHODS FOR TIME-DEPENDENT PROBLEMS.

By Jan S. Hesthaven, Sigal Gottlieb, David I. Gottlieb. 2007

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View Paper: https://www.semanticscholar.org/paper/3ba32fc629e0ded00b09e06dbc53c0ef8b127ab1

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In Numerical Analysis

Citations in the corpus

On Sobolev orthogonal polynomials (2014, positive): “Approximations using orthogonal expansions in Sobolev spaces have been extensively studied by spectral methods community; see, for example, [24] and numerous books (for example, [17, 23, 47]) on the subject, although Sobolev orthogonal polynomials are not often used or used only implicitly.”
The Müntz-Legendre Tau method for fractional differential equations (2016, methodology): “All of these methods can be derived from a weighted residual method[21, 37, 22].”
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks (2020, background): “where f̂k is the Fourier coefficient corresponding to the wave-number k [43].”
Ensemble Kalman methods for inverse problems (2012, methodology): “Spatially, a Galerkin spectral method [17] is used, in the same basis, and the convolutions arising from products in the nonlinear term are computed via FFTs.”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “Higher-order approximations are used in the p-version of the finite element method [175, 176] and spectral element methods [31,32,71,88].”
Accurate reconstruction of discontinuous functions using the singular pade-chebyshev method (2012, background): “INTRODUCTION Approximation of smooth functions by Fourier series or by truncated orthogonal polynomial expansions in general is known to be exponentially convergent and highly accurate ([2], [6]).”
Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients (2015, background): “Spectral approximations, such as the Fourier approximation based upon trigonometric polynomials for periodic problems, and the Chebyshev, Legendre, or the general Gegenbauer approximation based upon polynomials for nonperiodic problems are exponentially accurate for analytic functions [20–23].”