Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 693-707 |
| Seitenumfang | 15 |
| Fachzeitschrift | Computational Methods in Applied Mathematics |
| Jahrgang | 21 |
| Ausgabenummer | 3 |
| Frühes Online-Datum | 5 Juni 2021 |
| Publikationsstatus | Veröffentlicht - 1 Juli 2021 |
Abstract
In this work, goal-oriented adjoint-based a posteriori error estimates are derived for a nonlinear phase-field discontinuity problem in which a scalar-valued displacement field interacts with a scalar-valued smoothed indicator function. The latter is subject to an irreversibility constraint, which is regularized using a simple penalization strategy. The main advancements in the current work are error identities, resulting estimators, and two-sided estimates employing the dual-weighted residual method, which address the influence of the phase-field regularization, penalization, and spatial discretization parameters. Some numerical tests accompany our derived estimates.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Computational Methods in Applied Mathematics, Jahrgang 21, Nr. 3, 01.07.2021, S. 693-707.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Dual-Weighted Residual A Posteriori Error Estimates for a Penalized Phase-Field Slit Discontinuity Problem
AU - Wick, Thomas
PY - 2021/7/1
Y1 - 2021/7/1
N2 - In this work, goal-oriented adjoint-based a posteriori error estimates are derived for a nonlinear phase-field discontinuity problem in which a scalar-valued displacement field interacts with a scalar-valued smoothed indicator function. The latter is subject to an irreversibility constraint, which is regularized using a simple penalization strategy. The main advancements in the current work are error identities, resulting estimators, and two-sided estimates employing the dual-weighted residual method, which address the influence of the phase-field regularization, penalization, and spatial discretization parameters. Some numerical tests accompany our derived estimates.
AB - In this work, goal-oriented adjoint-based a posteriori error estimates are derived for a nonlinear phase-field discontinuity problem in which a scalar-valued displacement field interacts with a scalar-valued smoothed indicator function. The latter is subject to an irreversibility constraint, which is regularized using a simple penalization strategy. The main advancements in the current work are error identities, resulting estimators, and two-sided estimates employing the dual-weighted residual method, which address the influence of the phase-field regularization, penalization, and spatial discretization parameters. Some numerical tests accompany our derived estimates.
KW - Dual-Weighted Residuals
KW - Goal-Oriented Error Estimation
KW - Penalization
KW - Phase-Field Discontinuity
UR - http://www.scopus.com/inward/record.url?scp=85108117423&partnerID=8YFLogxK
U2 - 10.1515/cmam-2020-0038
DO - 10.1515/cmam-2020-0038
M3 - Article
AN - SCOPUS:85108117423
VL - 21
SP - 693
EP - 707
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 3
ER -