Abstract
In this chapter we present a fairly general approach to the stability and convergence analysis of spectral methods. We confine ourselves to linear problems. Analysis of several non-linear problems is presented in Chaps. 11 and 12. For time-dependent problems, only the discretizations in space are considered. Stability for fully discretized time-dependent problems is discussed in Chap. 4 by a classical eigenvalue analysis, and in Chap. 12 by variational methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A. (1988). Theory of Stability and Convergence for Spectral Methods. In: Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84108-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-84108-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52205-8
Online ISBN: 978-3-642-84108-8
eBook Packages: Springer Book Archive