Adaptive space-time goal-oriented methods for nonstationary fluid-structure interaction

In this project, first a space-time formulation (e.g., see [4]) of fluid-structure interaction [3,2] shall be developed. Therein, the temporal variable, based on a Galerkin discretization, can be split from the spatial discretization such that typical sequential time-stepping schemes are obtained [5]. Afterward, a space-time a goal-oriented error estimator based on dual-weighted residuals shall be derived. A crucial aspect is the efficient computation of the adjoint problem. On this basis, local error indicators for spatial and temporal refinements are extracted [5] (for incompressible Navier-Stokes) and [4] (for temporal refinements only). Since the overall problem is highly nonlinear, balancing of discretization and iteration errors may be a first option [1] (only for stationary problems so far); or a second option may be multigoal-oriented estimates; see again [1] or [6]. Having such a reliable computational framework, practical engineering problems shall be addressed in joint mathematical-engineering collaborations within the IRTG.

Doctoral Researcher: Julian Roth

Scientific Advisors: Thomas Wick, Ludovic Chamoin

1. B. Endtmayer, U. Langer, T. Wick; Multigoal-Oriented Error Estimates for Non-linear Problems, Journal of Numerical Mathematics (JNUM), Vol. 27(4), 2019, pp. 215-236
2. D. Jodlbauer, U. Langer, T. Wick; Parallel Block-Preconditioned Monolithic Solvers for Fluid-Structure-Interaction Problems, International Journal for Numerical Methods in Engineering, Vol. 117 (6), 2019, pp. 623-643
3. T. Richter; Fluid-Structure Interaction, Springer, 2017
4. L. Failer, T. Wick; Adaptive Time-Step Control for Nonlinear Fluid-Structure Interaction, Journal of Computational Physics (JCP), Vol. 366, 2018, pp. 448 - 477
5. M. Besier, R. Rannacher; Goal‐oriented space–time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow; International Journal for Numerical Methods in Fluids, Vol. 70, pp. 1139-1166, 2012
6. B. Endtmayer; Multi-goal oriented a posteriori error estimates for nonlinear partial differential equations, Dissertation, JKU Linz, Austria, pp. 197, 2020