Fourier Analysis of Finite Element Preconditioned Collocation Schemes

This p_per 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 tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes. IThls researchwas supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the author waz in residenceat the Institutefor Computer Applicationsin Scienceand Engineering (ICASE), NASA Langley Research Center,Hampton, VA 23665.