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dc.contributor.authorDarrigrand, V.
dc.contributor.authorRodríguez-Rozas, A.
dc.contributor.authorMuga, I.
dc.contributor.authorPardo, D. 
dc.contributor.authorRomkes, A.
dc.contributor.authorPrudhomme, S.
dc.description.abstractIn goal‐oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element‐wise error indicators that are used to drive optimal refinements. In this work, we propose to replace, in the error representation, the adjoint problem by an alternative operator. The main advantage of the proposed approach is that, when judiciously selecting such alternative operator, the corresponding upper bound of the error representation becomes sharper, leading to a more efficient goal‐oriented adaptivity. While the method can be applied to a variety of problems, we focus here on two‐ and three‐dimensional (2‐D and 3‐D) Helmholtz problems. We show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones and lead to a more robust p‐adaptive process. We also provide guidelines for finding operators delivering sharp error representation upper bounds. We further extend the results to a convection‐dominated diffusion problem as well as to problems with discontinuous material coefficients. Finally, we consider a sonic logging‐while‐drilling problem to illustrate the applicability of the proposed method.en_US
dc.description.sponsorshipV. Darrigrand, A. Rodriguez-Rozas and D. Pardo were partially funded by the Projects of the Spanish Ministry of Economy and Competitiveness with reference MTM2013-40824-P, MTM2016-76329-R (AEI/FEDER, EU), MTM2016-81697-ERC and the Basque Government Consolidated Research Group Grant IT649- 13 on “Mathematical Modeling, Simulation, and Industrial Applications (M2SI)”. A. Rodriguez-Rozas and D.Pardo were also partially funded by the BCAM “Severo Ochoa” accreditation of excellence SEV-2013-0323 and the Basque Government through the BERC2014-2017 program. A. Rodriguez-Rozas acknowledges support from Spanish Ministry under Grant No. FPDI- 2013-17098. I. Muga was partially funded by the FONDECYT project 1160774. The first four authors were also partially funded by the European Union’s Horizon 2020, research and innovation program under the Marie Sklodowska-Curie grant agreement No 644202. Serge Prudhomme is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjecterror representationen_US
dc.subjectfinite element methodsen_US
dc.subjectgoal-oriented adaptivityen_US
dc.subjectHelmholtz equationen_US
dc.titleGoal-oriented adaptivity using unconventional error representations for the multi-dimensional Helmholtz equationen_US
dc.journal.titleInternational Journal for Numerical Methods in Engineeringen_US

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