Computational Mechanics

, Volume 57, Issue 6, pp 1017–1035 | Cite as

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

  • Thomas WickEmail author
Original Paper


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.


Finite elements A posteriori error estimation  Dual weighted residuals Adaptivity Phase-field fracture 

Mathematics Subject Classification (2010)

65N30 65N50 49M15 35Q74 74R10 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  2. 2.Fakultät für Mathematik, Lehrstuhl M17Technische Universität MünchenGarching bei MünchenGermany

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