As we have seen in Chap. 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].
KeywordsBilinear Form Spectral Method Integration Formula Discontinuous Galerkin Spectral Element Method
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