Details
| Original language | English |
|---|---|
| Pages (from-to) | 192-208 |
| Number of pages | 17 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 279 |
| Publication status | Published - 1 May 2015 |
| Externally published | Yes |
Abstract
The dual weighted residual method (DWR) and its localization for mesh adaptivity applied to elliptic partial differential equations are investigated. The contribution of this paper is twofold: first, we introduce a novel localization technique based on the introduction of a partition of unity. This new technique is very easy to apply, as neither strong residuals nor jumps over element edges are required. Second, we compare and analyze (theoretically and numerically) different localization techniques used for mesh adaptivity with respect to their effectivity. Here, we focus on localizations in variational formulations that do not require the evaluation of the corresponding differential operator in the classical strong formulation. In our mathematical analysis, we show for different localization techniques (established methods and our new approach) that the local error indicators used for mesh adaptivity converge with proper order in the error functional. Several numerical tests substantiate our theoretical investigations.
Keywords
- Adaptivity, Adjoint, Dual weighted residuals, Error estimation, Finite elements
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 279, 01.05.2015, p. 192-208.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Variational localizations of the dual weighted residual estimator
AU - Richter, Thomas
AU - Wick, Thomas
N1 - Publisher Copyright: © 2014 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - The dual weighted residual method (DWR) and its localization for mesh adaptivity applied to elliptic partial differential equations are investigated. The contribution of this paper is twofold: first, we introduce a novel localization technique based on the introduction of a partition of unity. This new technique is very easy to apply, as neither strong residuals nor jumps over element edges are required. Second, we compare and analyze (theoretically and numerically) different localization techniques used for mesh adaptivity with respect to their effectivity. Here, we focus on localizations in variational formulations that do not require the evaluation of the corresponding differential operator in the classical strong formulation. In our mathematical analysis, we show for different localization techniques (established methods and our new approach) that the local error indicators used for mesh adaptivity converge with proper order in the error functional. Several numerical tests substantiate our theoretical investigations.
AB - The dual weighted residual method (DWR) and its localization for mesh adaptivity applied to elliptic partial differential equations are investigated. The contribution of this paper is twofold: first, we introduce a novel localization technique based on the introduction of a partition of unity. This new technique is very easy to apply, as neither strong residuals nor jumps over element edges are required. Second, we compare and analyze (theoretically and numerically) different localization techniques used for mesh adaptivity with respect to their effectivity. Here, we focus on localizations in variational formulations that do not require the evaluation of the corresponding differential operator in the classical strong formulation. In our mathematical analysis, we show for different localization techniques (established methods and our new approach) that the local error indicators used for mesh adaptivity converge with proper order in the error functional. Several numerical tests substantiate our theoretical investigations.
KW - Adaptivity
KW - Adjoint
KW - Dual weighted residuals
KW - Error estimation
KW - Finite elements
UR - http://www.scopus.com/inward/record.url?scp=84912553533&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2014.11.008
DO - 10.1016/j.cam.2014.11.008
M3 - Article
AN - SCOPUS:84912553533
VL - 279
SP - 192
EP - 208
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
ER -