KnowraSpectral methodLinked fromLinked fromThe 12 pages that link to Spectral method, each with the reason it gives.All 12Related 9Compared with 3Finite element methodCompared with: Global basis functions contrast with the local, element-by-element approximations typical of finite elements.Finite difference methodCompared with: Global basis functions can achieve high accuracy with fewer unknowns for sufficiently smooth solutions.Polynomial interpolationRelated: Polynomial interpolation supplies representations used in many spectral discretizations.Chebyshev polynomialsRelated: Chebyshev expansions provide a common basis for spectral calculations on bounded intervals.Finite volume methodCompared with: Its global basis contrasts with the local cell balances used by finite volumes.Fourier coefficientRelated: Unknown functions are represented by coefficients that numerical equations determine.Gibbs phenomenonRelated: Discontinuities in computed solutions can trigger Gibbs oscillations and reduce accuracy.Weierstrass approximation theoremRelated: Its polynomial bases rely on approximation capacity to represent smooth solutions accurately.Direct numerical simulationRelated: Spectral discretizations can accurately represent smooth turbulent fields with relatively few degrees of freedom.Parseval's identityRelated: The identity helps track norms and errors when computations move between physical and spectral representations.Method of linesRelated: Spectral approximations can provide the spatial discretization before time integration.Numerical methods for partial differential equationsRelated: It can achieve rapid accuracy for smooth solutions on suitable domains.