Spectral Filtering for Improved Performance of Collocation Discretization Methods

Abstract

Spectral filtering methods are investigated for use in reducing the Gibbs oscillations that result when discontinuous functions are projected onto globally definedtrial function expansions. Several physical-space filters are studied in the context of a high-degree, mixed collocation method used for time integration of a nonlinear boundary value problem with a piece-wise continuous, time-dependentboundary condition. Improved accuracy is reported, both in terms of point-wiseand norm-wise solution convergence, making the filtered global collocationapproach a potential alternative to spline formulations in some applications.