Revision as of 19:34, 21 August 2017 edit 192.76.8.83 (talk) changed often to potentially. Often is a meaningless term in this context. ← Previous edit		Revision as of 06:15, 11 August 2018 edit undo 27.253.251.94 (talk) →A relationship with the spectral element method: I fixed a confusing typo to explicitly show that thr constant C deepens n Tags: Mobile edit Mobile web edit Next edit →
Line 148: == A relationship with the spectral element method == One can show that if <math>g</math> is infinitely differentiable, then the numerical algorithm using Fast Fourier Transforms will converge faster than any polynomial in the grid size h. That is, for any n>0, there is a <math>CC_n<\infty</math> such that the error is less than <math>ChC_nh^n</math> for all sufficiently small values of <math>h</math>. We say that the spectral method is of order <math>n</math>, for every n>0. Because a [[spectral element method]] is a [[finite element method]] of very high order, there is a similarity in the convergence properties. However, whereas the spectral method is based on the eigendecomposition of the particular boundary value problem, the spectral element method does not use that information and works for arbitrary [[elliptic boundary value problem]]s.

Spectral method: Difference between revisions