Abstract
As we have seen in Chapter 4, when we approximate boundary-value problems using the finite element method, the order of convergence is anyhowlimited by the degree of the polynomials used, also in the case where solutions are very regular. In this chapter we will introduce spectral methods, for which the convergence rate is only limited by the regularity of the solution of the problem (and is exponential for analytical solutions). For a detailed analysis we refer to [CHQZ06, CHQZ07, Fun92, BM92].
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CITATION STYLE
Quarteroni, A. (2017). Spectral methods. In Modeling, Simulation and Applications (Vol. 16, pp. 225–266). Springer-Verlag Italia s.r.l. https://doi.org/10.1007/978-3-319-49316-9_10
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