Two-level Picard and modified Picard methods for the Navier-Stokes equations
type: Item
instance of: scholarly article
title: Two-level Picard and modified Picard methods for the Navier-Stokes equations
zbMATH Open document ID: 0828.76017
DOI: 10.1016/0096-3003(94)00134-P
published in: Applied Mathematics and Computation
publication date: 1995-10-22T00:00:00Z
review text: Iterative methods of Picard type for the Navier-Stokes equations are known to converge only for quite small Reynolds numbers. However, we study methods involving just one such iteration at general Reynolds numbers. For the initial approximation a coarse mesh of width \(h_0\) is used. The corrected approximation is computed by just one Picard or modified Picard step on a fine mesh of width \(h_1\). For example, \(h_1\) may be of order \(O(h^2_0)\) when linear velocity elements are used. The resulting method requires the solution of a (small) system of nonlinear equations on the coarse mesh and only one (larger) linear system on the fine mesh. This two-level Picard method is proven to converge for fixed Reynolds number as \(h\to 0\). Further, the fine mesh solution satisfies a quasi-optimal error bound.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 761791
zbMATH Keywords: finite element approximation
zbMATH Keywords: fine mesh solution
zbMATH Keywords: quasi-optimal error bound
author: William Layton
author: Wim Lenferink
MaRDI profile type: Publication
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full work available at URL: 0096-3003(94)00134-p
OpenAlex ID: W1989343938
description: scientific article; zbMATH DE number 761791