Fourier-analysis of Finite-element Preconditioned Collocation Schemes
(1992) SIAM Journal on Scientific and Statistical Computing — Vol. 13, n° 2, p. 596-610 (1992)
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- Abstract
- This paper investigates the spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the transverse direction) of the two-dimensional Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
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Deville, MO., & Mund, EH. (1992). Fourier-analysis of Finite-element Preconditioned Collocation Schemes. SIAM Journal on Scientific and Statistical Computing, 13(2), 596-610. https://doi.org/10.1137/0913033 (Original work published 1992)