A posteriori error estimation and error control for finite element approximations of the time-dependent Navier-Stokes equations

S. Prudhomme; J. T. Oden

doi:10.1016/S0168-874X(99)00048-7

A posteriori error estimation and error control for finite element approximations of the time-dependent Navier-Stokes equations

S. Prudhomme, J. T. Oden^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We present an approach to estimate numerical errors in finite element approximations of the timedependent Navier-Stokes equations along with a strategy to control these errors. The error estimators and the error control procedure are based on the residuals of the Navier-Stokes equations, which are shown to be comparable to error components in the velocity variable. The present methodology applies to the estimation of numerical errors due to the spatial discretization only. Its performance is demonstrated for twodimensional channel flows past a cylinder in the periodic regime. copy; 1999 Elsevier Science B.V. All rights reserved.

Original language	English (US)
Pages (from-to)	247-262
Number of pages	16
Journal	Finite Elements in Analysis and Design
Volume	33
Issue number	4
DOIs	https://doi.org/10.1016/S0168-874X(99)00048-7
State	Published - Nov 15 1999
Externally published	Yes

Keywords

A posteriori estimation
Mesh adaptation
Navier-stokes equations

ASJC Scopus subject areas

Analysis
General Engineering
Computer Graphics and Computer-Aided Design
Applied Mathematics

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10.1016/S0168-874X(99)00048-7

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abstract = "We present an approach to estimate numerical errors in finite element approximations of the timedependent Navier-Stokes equations along with a strategy to control these errors. The error estimators and the error control procedure are based on the residuals of the Navier-Stokes equations, which are shown to be comparable to error components in the velocity variable. The present methodology applies to the estimation of numerical errors due to the spatial discretization only. Its performance is demonstrated for twodimensional channel flows past a cylinder in the periodic regime. copy; 1999 Elsevier Science B.V. All rights reserved.",

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AU - Prudhomme, S.

AU - Oden, J. T.

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Y1 - 1999/11/15

N2 - We present an approach to estimate numerical errors in finite element approximations of the timedependent Navier-Stokes equations along with a strategy to control these errors. The error estimators and the error control procedure are based on the residuals of the Navier-Stokes equations, which are shown to be comparable to error components in the velocity variable. The present methodology applies to the estimation of numerical errors due to the spatial discretization only. Its performance is demonstrated for twodimensional channel flows past a cylinder in the periodic regime. copy; 1999 Elsevier Science B.V. All rights reserved.

AB - We present an approach to estimate numerical errors in finite element approximations of the timedependent Navier-Stokes equations along with a strategy to control these errors. The error estimators and the error control procedure are based on the residuals of the Navier-Stokes equations, which are shown to be comparable to error components in the velocity variable. The present methodology applies to the estimation of numerical errors due to the spatial discretization only. Its performance is demonstrated for twodimensional channel flows past a cylinder in the periodic regime. copy; 1999 Elsevier Science B.V. All rights reserved.

KW - A posteriori estimation

KW - Mesh adaptation

KW - Navier-stokes equations

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JO - Finite Elements in Analysis and Design

JF - Finite Elements in Analysis and Design

IS - 4

ER -

A posteriori error estimation and error control for finite element approximations of the time-dependent Navier-Stokes equations

Abstract

Keywords

ASJC Scopus subject areas

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