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A posteriori error estimators for the Stokes equations


Verfürth, R (1989). A posteriori error estimators for the Stokes equations. Numerische Mathematik, 55(3):309-325.

Abstract

We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.

Abstract

We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1989
Deposited On:29 Nov 2010 16:29
Last Modified:06 Dec 2017 21:14
Publisher:Springer
ISSN:0029-599X
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/BF01390056
Related URLs:http://www.digizeitschriften.de/dms/img/?PPN=PPN362160546_0055&DMDID=dmdlog20

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