V. Kosin, A. Fau, F. Hild, T. Wick
This work focuses on temporal adaptivity for phase-field fracture problems. The methodology requires a space-time formulation and utilizes a space-time Galerkin finite element discretization for the governing phase-field equations. Then, goal functionals (i.e., quantities of interest) are introduced. The computational implementation of goal-oriented error control employs the dual-weighted residual method in which an adjoint problem must be solved. As the analysis is quasi-static, without a temporal derivative, the adjoint problem of the quasistatic primal problem decouples in time. Nonetheless, time-averaged goal functionals can also be considered. The temporal errors are localized using a partition of unity, which allows one to adaptively refine and coarsen the time intervals in the space-time cylinder. Numerical tests are performed on a single edge notched tensile test to investigate the quality of the proposed error estimator.
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Published on 28/06/24Accepted on 28/06/24Submitted on 28/06/24
Volume Multiscale and Multiphysics Systems, 2024DOI: 10.23967/wccm.2024.035Licence: CC BY-NC-SA license
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