Goal‐oriented error estimation for Stokes flow interacting with a flexible channel

Abstract

AbstractWe 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.