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In this contribution, we revisit adjoint formulations for stationary and nonstationary space-time fluid-structure interaction. The adjoints serve for two purposes: goal-oriented a posteriori error estimation with the dual-weighted residual method and gradient-based numerical optimization. Our developments are substantiated with comments on numerical simulations in some other published studies.

In this work we examine the viability of Rosenbrock-type time-stepping methods - specifically Rosenbrock-Wanner (ROW) methods and W-methods - for the temporal discretization of certain parabolic partial differential equations (PDEs) that have a dominating linear term (usually the Laplacian) and lower order nonlinearities, such as convective or reactive terms. In dieser Arbeit untersuchen wir die Eignung von Rosenbrock-Typ-Methoden (RTM) - speziell von Rosenbrock-Wanner- (ROW) und W-Methoden - für die zeitliche Diskretisierung von bestimmten parabolischen partiellen Differentialgleichungen (PDG), die einen dominierenden linearen Term haben (z. B. den Laplace-Operator) und Nichtlinearitäten niedrigerer Ordnung, wie z. B. konvektive oder reaktive Terme.