Details
| Original language | English |
|---|---|
| Pages (from-to) | 753-776 |
| Number of pages | 24 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 18 |
| Issue number | 4 |
| Publication status | Published - 1 Oct 2018 |
| Externally published | Yes |
Abstract
In this work, we realize goal-oriented error estimation using the dual-weighted residual method on general polygonal meshes. Such meshes are of current interest in various applications thanks to their great flexibility. Specifically the discrete problems are treated on BEM-based FEM. Our dual-weighted residual estimator is derived for two localization procedures. Firstly, a classical (strong) localization. Secondly, a weak form is adopted in which localization is achieved with the help of a partition-of-unity. The dual (i.e., adjoint) solution is obtained via a local higher-order approximation using a single element. Our algorithmic developments are substantiated with the help of several numerical tests.
Keywords
- BEM-Based FEM, Dual-Weighted Residual Estimator, Goal-Oriented A Posteriori Error Estimation, Partition-of-Unity, Polygonal Finite Elements
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational Methods in Applied Mathematics, Vol. 18, No. 4, 01.10.2018, p. 753-776.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Dual-Weighted Residual Estimator Realized on Polygonal Meshes
AU - Weißer, Steffen
AU - Wick, Thomas
N1 - Publisher Copyright: © 2018 Walter de Gruyter GmbH, Berlin/Boston. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - In this work, we realize goal-oriented error estimation using the dual-weighted residual method on general polygonal meshes. Such meshes are of current interest in various applications thanks to their great flexibility. Specifically the discrete problems are treated on BEM-based FEM. Our dual-weighted residual estimator is derived for two localization procedures. Firstly, a classical (strong) localization. Secondly, a weak form is adopted in which localization is achieved with the help of a partition-of-unity. The dual (i.e., adjoint) solution is obtained via a local higher-order approximation using a single element. Our algorithmic developments are substantiated with the help of several numerical tests.
AB - In this work, we realize goal-oriented error estimation using the dual-weighted residual method on general polygonal meshes. Such meshes are of current interest in various applications thanks to their great flexibility. Specifically the discrete problems are treated on BEM-based FEM. Our dual-weighted residual estimator is derived for two localization procedures. Firstly, a classical (strong) localization. Secondly, a weak form is adopted in which localization is achieved with the help of a partition-of-unity. The dual (i.e., adjoint) solution is obtained via a local higher-order approximation using a single element. Our algorithmic developments are substantiated with the help of several numerical tests.
KW - BEM-Based FEM
KW - Dual-Weighted Residual Estimator
KW - Goal-Oriented A Posteriori Error Estimation
KW - Partition-of-Unity
KW - Polygonal Finite Elements
UR - http://www.scopus.com/inward/record.url?scp=85037707281&partnerID=8YFLogxK
U2 - 10.1515/cmam-2017-0046
DO - 10.1515/cmam-2017-0046
M3 - Article
AN - SCOPUS:85037707281
VL - 18
SP - 753
EP - 776
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 4
ER -