Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

[EN] In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction (FSI). The a posteriori error estimator is accomplished using the dual-weighted residual method in which the adjoint equation arises. The fluid-structure interaction problem is formulated within a variational-monolithic framework using arbitrary Lagrangian-Eulerian coordinates. The overall problem is nonlinear and solved with Newton’s method. We specifically consider the FSI-1 benchmark problem in which quantities of interest include the elastic beam displacements, drag, and lift. The implementation is based on the deal.II finite element library and provided open-source published on github https://github.com/tommeswick/goal-oriented-fsi. Possible extensions are discussed in the source code and in the conclusions of this paper. ; This work is supported by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). ; Wick, T. (2022). Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 257-266. https://doi.org/10.4995/YIC2021.2021.12332 ; 257 ; 266