Year: 2008
Type: article
Abstract: We discuss the impact of modal filtering in Legendre spectral methods, both on accuracy and stability. For the former, we derive sufficient conditions on the filter to recover high order accuracy away from points of discontinuity. Computational results confirm that less strict necessary conditions appear to be adequate. We proceed to discuss a instability mechanism in polynomial spectral methods and prove that filtering suffices to ensure stability. The results are illustrated by computational experiments.
Source: Mathematics of Computation
Authors: Jan Hesthaven, Robert Kirby
Institutions: Brown University, University of Utah
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Awards: US-France Cooperative Research (INRIA): Approximate Boundary Conditions for Computational Wave Problems, CAREER: Towards Robust and Efficient High-Order Adaptive Computational Methods for Conservation Laws in Complex Geometries -- Analysis, Implementation, and Applications, CAREER: Quantifying and Controlling Error and Uncertainty in Computational Inverse Problems, G8340637458
OpenAlex ID: W2041145218