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Goal-oriented error estimation and adaptivity for fluid-structure interaction

Kris van der Zee
Eindhoven University of Technology


Goal-oriented methods embrace the notion that numerical simulations are generally performed to study specific features of solutions, and not necessarily the solution itself. Such features are the so-called output quantities of interest and represent the goals of the computation. Obviously, it is important to estimate the discretization error in such quantities of interest, and to use these estimates to perform adaptive mesh-refinement in order to control their accuracy.

In this talk we consider the application of goal-oriented methods to steady fluid-structure interaction. The fundamental complication concerns the derivation of the dual (linearized-adjoint) problem required for the computation of goal-oriented error estimates. Since fluid-structure interaction is a free-boundary problem, the linearization of the geometric nonlinearity is nontrivial. Using techniques from shape differential calculus we show that the linearized adjoint corresponds to a coupled fluid-structure problem with nonstandard coupling conditions. Furthermore, we present numerical experiments where we employ these linearized adjoints in goal-oriented error estimation and adaptivity.

Joint work with: Ido Akkerman, Rene de Borst, and Harald van Brummelen

Thursday, October 4, 2012
11:00AM AP&M 2402