A Partition-of-Unity Dual-Weighted Residual Approach for Multi-Objective Goal Functional Error Estimation Applied to Elliptic Problems
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 impl...
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| Vydáno v: | Journal of computational methods in applied mathematics Ročník 17; číslo 4; s. 575 - 599 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Minsk
De Gruyter
01.10.2017
Walter de Gruyter GmbH |
| Témata: | |
| ISSN: | 1609-4840, 1609-9389 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1609-4840 1609-9389 |
| DOI: | 10.1515/cmam-2017-0001 |