Details
| Original language | English |
|---|---|
| Pages (from-to) | 693-707 |
| Number of pages | 15 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 21 |
| Issue number | 3 |
| Early online date | 5 Jun 2021 |
| Publication status | Published - 1 Jul 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.
Keywords
- Dual-Weighted Residuals, Goal-Oriented Error Estimation, Penalization, Phase-Field Discontinuity
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computational Methods in Applied Mathematics, Vol. 21, No. 3, 01.07.2021, p. 693-707.
Research output: Contribution to journal › Article › Research › 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 -