Abstract
As we have seen in Chapter 4, when we approximate boundary-value problems using the finite element method, the order of convergence is anyhow limited 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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Notes
- 1.
1 From now on, for simplicity of notation, we will denote the G-NI solution by u N (instead of \(u^*_N\)), since there is no longer the risk to confuse it with the spectral solution.
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© 2014 Springer-Verlag Italia
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Quarteroni, A. (2014). Spectral methods. In: Numerical Models for Differential Problems. MS&A - Modeling, Simulation and Applications, vol 8. Springer, Milano. https://doi.org/10.1007/978-88-470-5522-3_10
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DOI: https://doi.org/10.1007/978-88-470-5522-3_10
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-5521-6
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