Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Van der Zee, K.G.
Van Brummelen, E.H.
De Borst, R.

2006-09-06

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest. However, the free-boundary character of fluid-structure-interaction problems forms a fundamental complication, as it yields the underlying domain unknown a-priori. Instead, the domain comprises part of the solution. Consequently, the well-established generic framework for dual-based error estimation is not applicable. In this work we develop a framework for dual-based a-posteriori error estimation for free-boundary problems such as fluid-structure interaction. The framework is based on the embedded-domain approach and an extension operator which enables the comparison of approximate solutions on distinct domains. Given an approximate fluid and structure solution, we present a dual problem on the corresponding approximate fluid domain. Finally, we employ the dual solution to present an exact error representation formula.

fluid-structure interaction
free-boundary problems
a-posteriori error estimation
goal-oriented error estimation
dual-based error estimation
adaptive finite element method

http://resolver.tudelft.nl/uuid:f1cf2206-cd9c-400a-a6a1-18f549f967e6

Conference proceedings

conference paper

(c) 2006 Van der Zee, K.G.; Van Brummelen, E.H.; De Borst, R.