Spectral filtering for improved performance of collocation discretization methods

Spectral filtering methods are investigated for reducing the Gibbs oscillations that result when discontinuous functions are projected onto globally defined trial function expansions. Several physical-space filters are studied to examine which is best suited to high-degree, mixed collocation methods used for time integration of non-linear boundary value problems with piece-wise continuous, time-dependent boundary conditions. Accuracy of the filtered global collocation methods relative to the non-filtered approaches is both in terms of point-wise and norm-wise solution convergence, making the filtered global collocation approach a potential alternative to spline formulations for some time integration applications. (C) 2001 Elsevier Science Ltd. All rights reserved.