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Goal‐oriented error estimation for Stokes flow interacting with a flexible channel
Author(s) -
van der Zee K. G.,
van Brummelen E. H.,
de Borst R.
Publication year - 2007
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1652
Subject(s) - estimator , channel (broadcasting) , stokes flow , domain (mathematical analysis) , flow (mathematics) , mathematics , stokes problem , dual (grammatical number) , open channel flow , variable (mathematics) , finite element method , computer science , mathematical optimization , algorithm , mathematical analysis , geometry , physics , telecommunications , statistics , art , literature , thermodynamics
We develop a goal‐oriented error estimator for finite‐element discretizations of fluid–structure‐interaction problems. As a model problem, we consider the steady Stokes flow in a 2D channel where part of the channel wall is flexible. We introduce the reference domain approach where the Stokes problem on the variable domain is transformed into a fixed reference domain. This allows the formulation of a proper dual problem. The dual solution is then used in the evaluation of the error estimate, as usual. Copyright © 2007 John Wiley & Sons, Ltd.