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Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity

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Abstract

In this study, a posteriori error estimation and goal-oriented mesh adaptivity are developed for phase-field fracture propagation. Goal functionals are computed with the dual-weighted residual (DWR) method, which is realized by a recently introduced novel localization technique based on a partition-of-unity (PU). This technique is straightforward to apply since the weak residual is used. The influence of neighboring cells is gathered by the PU. Consequently, neither strong residuals nor jumps over element edges are required. Therefore, this approach facilitates the application of the DWR method to coupled (nonlinear) multiphysics problems such as fracture propagation. These developments then allow for a systematic investigation of the discretization error for certain quantities of interest. Specifically, our focus on the relationship between the phase-field regularization and the spatial discretization parameter in terms of goal functional evaluations is novel.

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Acknowledgments

I wish to thank the reviewers for their critical comments that helped to improve the manuscript. Moreover, I am grateful to Ivo Babuska (ICES, UT Austin) for very initial discussions on error estimation of finite element discretizations for fracture modeling during my 2-year-stay at ICES from 2012 to 2014. The same acknowledgments go to Franz-Theo Suttmeier (Univ. Siegen) who gave some hints to mesh adaptation strategies for quasi-stationary evolution problems. Finally, I thank Mary F. Wheeler (ICES, UT Austin) and Andro Mikelić (Univ. Lyon) for our joint start on phase-field fracture modeling in poroelasticity and in particular pressurized fracture techniques.

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  1. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Str. 69, 4040, Linz, Austria

    Thomas Wick

  2. Fakultät für Mathematik, Lehrstuhl M17, Technische Universität München, Boltzmannstr. 3, 85747, Garching bei München, Germany

    Thomas Wick

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Wick, T. Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity. Comput Mech 57, 1017–1035 (2016). https://doi.org/10.1007/s00466-016-1275-1

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