On fast direct Poisson solver, inf-sup constant and iterative Stokes solver by Legendre-Galerkin method
type: Item
instance of: scholarly article
title: On fast direct Poisson solver, inf-sup constant and iterative Stokes solver by Legendre-Galerkin method
zbMATH Open document ID: 0822.65083
author: Jie Shen
published in: Journal of Computational Physics
publication date: 1995-04-05T00:00:00Z
review text: This paper dealts with a fast Poisson solver and an iterative Stokes solver whose complexities are respectively \(O(N^ 2\log_ 2 N)\) and \(O(N^{5/2}\log_ 2 N)\) in a two-dimensional rectangular domain (\(N\) is the cutoff number of the polynomial expansion in each direction). Both solvers are based on the Legendre-Galerkin approximation. For a sequence of the discretized Stokes systems the author studies numerically the behaviour of the Babuska-Brezzi inf-sup constant \(\beta_{N, m}\) \((m= N, N- 1, N-2,\dots)\). As is well-known the discretized system admits a unique solution if and only if \(\beta_{N, m}> 0\). The behaviour of these constants are also important because the error estimate is optimal if and only if \(\beta_{N, m}\) are independent of \((N, m)\), and the number of iterations in the conjugate Uzawa method is proportional to \(\beta_{N, m}\). The results presented may serve as a reference for users of spectral methods to choose an appropriate pair \((N, m)\) of discretization spaces in the Stokes problem.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 740621
zbMATH Keywords: fast Poisson solver
zbMATH Keywords: iterative Stokes solver
zbMATH Keywords: Legendre-Galerkin approximation
zbMATH Keywords: Babuska-Brezzi inf-sup constant
zbMATH Keywords: error estimate
zbMATH Keywords: conjugate Uzawa method
zbMATH Keywords: spectral methods
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
full work available at URL: jcph.1995.1017
OpenAlex ID: W2089984340
DOI: 10.1006/JCPH.1995.1017
description: scientific article; zbMATH DE number 740621