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Error Control and Adaptivity for the Finite Cell Method

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Non-standard Discretisation Methods in Solid Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 98))

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Abstract

In this work, we discuss a posteriori error control and adaptivity in the setting of the finite cell method (FCM). For this purpose, we introduce k-times differentiable basis functions for hp-adaptive meshes consisting of paraxial rectangles with arbitrary-level hanging nodes suitable for the immersed-boundary setting of the FCM. Furthermore, we present error control for Poisson’s problem in the context of the finite cell method. To this end, we establish a reliable residual-based estimator for the energy error. Additionally, we introduce a dual-weighted residual estimator capable of separating the discretization error from the quadrature error which poses a second error source typically arising in the FCM. Several numerical experiments illustrate the reliability and efficiency properties of the estimators.

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Acknowledgements

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SCHR 1244/4-2 – SPP 1748.

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  1. Fachbereich Mathematik, Paris Lodron Universität Salzburg, Hellbrunner Straße 34, 5020, Salzburg, Austria

    Paolo Di Stolfo & Andreas Schröder

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  1. Paolo Di Stolfo
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Correspondence to Andreas Schröder .

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  1. Institute of Mechanics, University of Duisburg-Essen, Essen, Germany

    Jörg Schröder

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

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Di Stolfo, P., Schröder, A. (2022). Error Control and Adaptivity for the Finite Cell Method. In: Schröder, J., Wriggers, P. (eds) Non-standard Discretisation Methods in Solid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-92672-4_14

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  • DOI: https://doi.org/10.1007/978-3-030-92672-4_14

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