Spectral filtering for improved performance of collocation discretization methods

Spectral filtering methods are investigated for reducing the Gibbs oscillat ions that result when discontinuous functions are projected onto globally d efined trial function expansions. Several physical-space filters are studie d 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 filte red global collocation methods relative to the non-filtered approaches is b oth in terms of point-wise and norm-wise solution convergence, making the f iltered global collocation approach a potential alternative to spline formu lations for some time integration applications. (C) 2001 Elsevier Science L td. All rights reserved.