FOURIER-ANALYSIS OF FINITE-ELEMENT PRECONDITIONED COLLOCATION SCHEMES

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.