Details
| Original language | English |
|---|---|
| Pages (from-to) | 575-599 |
| Number of pages | 25 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 17 |
| Issue number | 4 |
| Publication status | Published - 1 Oct 2017 |
| Externally published | Yes |
Abstract
In this work, we design a posteriori error estimation and mesh adaptivity for multiple goal functionals. Our method is based on a dual-weighted residual approach in which localization is achieved in a variational form using a partition-of-unity. The key advantage is that the method is simple to implement and backward integration by parts is not required. For treating multiple goal functionals we employ the adjoint to the adjoint problem (i.e., a discrete error problem) and suggest an alternative way for its computation. Our algorithmic developments are substantiated for elliptic problems in terms of four different numerical tests that cover various types of challenges, such as singularities, different boundary conditions, and diverse goal functionals. Moreover, several computations with higher-order finite elements are performed.
Keywords
- Adjoint to the Adjoint Problem, Dual-Weighted Residual, Finite Element Method, Mesh Adaptivity, Multi-Objective Goal Functionals, Partition-of-Unity
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. 17, No. 4, 01.10.2017, p. 575-599.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Partition-of-Unity Dual-Weighted Residual Approach for Multi-Objective Goal Functional Error Estimation Applied to Elliptic Problems
AU - Endtmayer, Bernhard
AU - Wick, Thomas
N1 - Publisher Copyright: © 2017 Walter de Gruyter GmbH, Berlin/Boston. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - In this work, we design a posteriori error estimation and mesh adaptivity for multiple goal functionals. Our method is based on a dual-weighted residual approach in which localization is achieved in a variational form using a partition-of-unity. The key advantage is that the method is simple to implement and backward integration by parts is not required. For treating multiple goal functionals we employ the adjoint to the adjoint problem (i.e., a discrete error problem) and suggest an alternative way for its computation. Our algorithmic developments are substantiated for elliptic problems in terms of four different numerical tests that cover various types of challenges, such as singularities, different boundary conditions, and diverse goal functionals. Moreover, several computations with higher-order finite elements are performed.
AB - In this work, we design a posteriori error estimation and mesh adaptivity for multiple goal functionals. Our method is based on a dual-weighted residual approach in which localization is achieved in a variational form using a partition-of-unity. The key advantage is that the method is simple to implement and backward integration by parts is not required. For treating multiple goal functionals we employ the adjoint to the adjoint problem (i.e., a discrete error problem) and suggest an alternative way for its computation. Our algorithmic developments are substantiated for elliptic problems in terms of four different numerical tests that cover various types of challenges, such as singularities, different boundary conditions, and diverse goal functionals. Moreover, several computations with higher-order finite elements are performed.
KW - Adjoint to the Adjoint Problem
KW - Dual-Weighted Residual
KW - Finite Element Method
KW - Mesh Adaptivity
KW - Multi-Objective Goal Functionals
KW - Partition-of-Unity
UR - http://www.scopus.com/inward/record.url?scp=85030990697&partnerID=8YFLogxK
U2 - 10.1515/cmam-2017-0001
DO - 10.1515/cmam-2017-0001
M3 - Article
AN - SCOPUS:85030990697
VL - 17
SP - 575
EP - 599
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 4
ER -