Spectral approximation of the periodic nonperiodic Navier-Stokes equations
type: Item
instance of: scholarly article
title: Spectral approximation of the periodic nonperiodic Navier-Stokes equations
zbMATH Open document ID: 0583.65085
DOI: 10.1007/BF01400175
author: Christine Bernardi
author: Yvon Maday
author: Brigitte Métivet
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133219
review text: In order to approximate the Navier-Stokes equations with periodic boundary conditions in two directions and a no-slip boundary condition in the third direction by spectral methods, we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure. The compatibility between these two spaces is checked via an inf-sup condition. We analyze a spectral and a collocation pseudo- spectral method for the Stokes problem and a collocation pseudo-spectral method for the Navier-Stokes equations. We derive error bounds of spectral type, i.e. which behave like \(M^{-\sigma}\), where M depends on the number of degrees of freedom of the method and \(\sigma\) represents the regularity of the data.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N35
zbMATH DE Number: 3934370
zbMATH Keywords: periodic boundary conditions
zbMATH Keywords: spectral methods
zbMATH Keywords: collocation pseudo- spectral method
zbMATH Keywords: Stokes problem
zbMATH Keywords: error bounds
zbMATH Keywords: staggered grids
MaRDI profile type: Publication
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OpenAlex ID: W2072376976
description: scientific article; zbMATH DE number 3934370