Spectral Methods: Fundamentals in Single Domains

By C. Canuto, M. Hussaini, Alfio Maria Quarteroni, Thomas A. Zang. 2010

2,243 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/88278f7cb429464daa319d82744f2a5c97d467f2

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Citations in the corpus

Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed (2010, unknown): “[2, 10].”
Spectral technique for solving variable‐order fractional Volterra integro‐differential equations (2018, methodology): “For each spectral method, we formulate the unknown solution as a truncated sum of certain basic functions and then to select the coefficients with a view to minimize the difference between the exact and numerical solutions as possible [54].”
Visualizing the geometry of state space in plane Couette flow (2007, methodology): “wo of the three functions Φu σkjl,Φ v σkjl,Φ w σkjl can be set independently and the third derived from incompressibility. These two possibilities are distinguished with the index σ ∈{0,1}. Following Canuto et al. (2006), we prescribe the no-slip conditions by deﬁning the polynomial triplets as diﬀe”
Pseudospectrum and Black Hole Quasinormal Mode Instability (2020, methodology): “Spectral methods provide well-adapted tools for these calculations [4, 52, 53].”
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].”
A review of operational matrices and spectral techniques for fractional calculus (2015, unknown): “and infinite intervals [36–47].”
Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, unknown): “Then, for all v ∈ H(Λ) ∩ H(1) 0(Λ), m ≥ 1, the following optimal error estimates hold (see [2]): Π 1,0 M v− v 1,Λ ® M1−m ‖v‖m,Λ , (4.”
Jacobi spectral solution for integral algebraic equations of index-2 (2011, methodology): “Our strategy is mainly based on the ideas in [20], together with the following auxiliary lemmas from [6] and [7]: Lemma 2.”
The Sun’s Supergranulation (2010, methodology): “High-resolution simulations using spectral methods (Canuto et al. 2006) remain the most adequate tool to reach highly-supercritical regimes.”
Some Recent Advances on Spectral Methods for Unbounded Domains (2009, background): “…in the early years on the error analysis of these methods (see, e.g. [6, 7, 15, 20, 23, 42]), it is only in the last ten years or so that the basic approximation properties of these orthogonal systems, and their applications to PDEs, were systematically studied (cf. [13] for a brief account).”
Comparisons of p-adaptation strategies based on truncation- and discretisation-errors for high order discontinuous Galerkin methods (2016, background): “X el2 h R N(uN) = 0, (2) where is the test function, uN represents the discrete solution of the PDE, N is the degree of the polynomial used to represent the solution inside each spectral element el 2 h and RN represents the discrete spatial partial differential operator.”
On shifted Jacobi spectral method for high-order multi-point boundary value problems (2012, methodology): “Spectral methods are a widely used tool in the solution of differential equations, function approximation and variational problems [7,17].”