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A posteriori error estimation in model order reduction of elastic multibody systems with large rigid motion. (English) Zbl 1425.74452

Fehr, Jörg (ed.) et al., IUTAM symposium on model order reduction of coupled systems. MORCOS 2018. Proceedings of the IUTAM symposium, Stuttgart, Germany, May 22–25, 2018. Cham: Springer. IUTAM Bookser. 36, 95-110 (2020).
Summary: We consider the equation of motion of an elastic multibody system in absolute coordinate formulation (ACF). The resulting nonlinear second order DAE of index two has a unique solution and is reduced using the strong POD-greedy method. The reduced model is certified by deriving a posteriori error estimators, which are independent of the model order reduction (MOR) method used to obtain the projection basis. The first error estimation technique, which we establish in this paper, is a first order linear integro-differential equation. It relies on the gradient of a function and can be integrated along with the reduced simulation (in-situ). The second error estimation technique is hierarchical and requires a more enriched basis in order to estimate the error in the solution due to a coarser basis. To verify and illustrate the efficacy of the estimators, reproductive and predictive numerical experiments are performed on a coupled elastic multibody system consisting of a double elastic pendulum.
For the entire collection see [Zbl 1425.93009].

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Software:

IDSOLVER
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References:

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