@article{Kanevsky:190461, title = {Idempotent filtering in spectral and spectral element methods}, author = {Kanevsky, Alex and Carpenter, Mark H. and Hesthaven, Jan S.}, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, journal = {Journal of Computational Physics}, number = {1}, volume = {220}, pages = {41-58}, year = {2006}, abstract = {The comparison of numerical results for implicit-explicit and fully explicit Runge-Kutta time integration methods for a nozzle flow problem shows that filtering can significantly degrade the accuracy of the numerical solution for long-time integration problems. We demonstrate analytically and numerically that filtering-in-time errors become additive for parallel to u(N)(x, t + k Delta t) - u(N)(x, t)parallel to << parallel to u(N)(x, t)parallel to when nonidempotent filters are used, and suggest the development and implementation of idempotent filters. (c) 2006 Elsevier Inc. All rights reserved.}, }