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arXiv · 2202.08763

Residual-based error estimation and adaptivity for stabilized immersed isogeometric analysis using truncated hierarchical B-splines

Sai C. Divi·Pieter H. van Zuijlen·Tuong Hoang·Frits de Prenter·Ferdinando Auricchio·Alessandro Reali·E. Harald van Brummelen·Clemens V. Verhoosel
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Abstract

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been tailored to the immersed setting by the incorporation of appropriately scaled stabilization and boundary terms. Element-wise error indicators are elaborated for the Laplace and Stokes problems, and a THB-spline-based local mesh refinement strategy is proposed. The error estimation .and adaptivity procedure is applied to a series of benchmark problems, demonstrating the suitability of the technique for a range of smooth and non-smooth problems. The adaptivity strategy is also integrated in a scan-based analysis workflow, capable of generating reliable, error-controlled, results from scan data, without the need for extensive user interactions or interventions.

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Sai C. Divi, Pieter H. van Zuijlen, Tuong Hoang, Frits de Prenter, Ferdinando Auricchio, Alessandro Reali, E. Harald van Brummelen, Clemens V. Verhoosel. 2022-02-17. Residual-based error estimation and adaptivity for stabilized immersed isogeometric analysis using truncated hierarchical B-splines. https://doi.org/10.1093/jom%2Fufac015

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