A Legendre spectral element method for eigenvalues in hydrodynamic stability

Hill, Antony A.; Straughan, B.

Abstract

A Legendre polynomial-based spectral technique is developed to be applicable to solving eigenvalue problems which arise in linear and nonlinear stability questions in porous media, and other areas of Continuum Mechanics. The matrices produced in the corresponding generalised eigenvalue problem are sparse, reducing the computational and storage costs, where the superimposition of boundary conditions is not needed due to the structure of the method. Several eigenvalue problems are solved using both the Legendre polynomial-based and Chebyshev tau techniques. In each example, the Legendre polynomial-based spectral technique converges to the required accuracy utilising less polynomials than the Chebyshev tau method, and with much greater computational efficiency. © 2005 Elsevier B.V. All rights reserved.

Citation

Hill, A. A., & Straughan, B. (2006). A Legendre spectral element method for eigenvalues in hydrodynamic stability. Journal of Computational and Applied Mathematics, 193(1), 363-381. https://doi.org/10.1016/j.cam.2005.06.011

• Journal Article Type: Article
• Publication Date: Aug 15, 2006
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 193
• Issue: 1
• Pages: 363-381
• DOI: https://doi.org/10.1016/j.cam.2005.06.011
• Keywords: spectral methods, porous media, sparse matrices, hydrodynamic stability
• Public URL: https://uwe-repository.worktribe.com/output/1044171
• Publisher URL: http://dx.doi.org/10.1016/j.cam.2005.06.011