Details
| Original language | English |
|---|---|
| Pages (from-to) | 1017-1035 |
| Number of pages | 19 |
| Journal | Computational mechanics |
| Volume | 57 |
| Issue number | 6 |
| Publication status | Published - 1 Jun 2016 |
| Externally published | Yes |
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.
Keywords
- A posteriori error estimation, Adaptivity, Dual weighted residuals, Finite elements, Phase-field fracture
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 57, No. 6, 01.06.2016, p. 1017-1035.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity
AU - Wick, Thomas
N1 - Publisher Copyright: © 2016, Springer-Verlag Berlin Heidelberg. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - 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.
AB - 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.
KW - A posteriori error estimation
KW - Adaptivity
KW - Dual weighted residuals
KW - Finite elements
KW - Phase-field fracture
UR - http://www.scopus.com/inward/record.url?scp=84960075195&partnerID=8YFLogxK
U2 - 10.1007/s00466-016-1275-1
DO - 10.1007/s00466-016-1275-1
M3 - Article
AN - SCOPUS:84960075195
VL - 57
SP - 1017
EP - 1035
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 6
ER -