131673 20241125101201.0 doi 10.1016/j.cma.2023.116341 sideral 137023 ART-2023-137023 eng Hauke, Guillermo Universidad de Zaragoza (orcid)0000-0001-7802-3411 A review of VMS a posteriori error estimation with emphasis in fluid mechanics 2023 Access copy available to the general public Unrestricted This article outlines the research on the application of the variational multiscale theory (VMS) to a posteriori error estimation. VMS theory was initially developed by Professor Hughes to evince the origins of stabilized methods. In this paper it is shown that the stabilization parameters and the stabilization terms contain true error information that can be used to obtain explicit and implicit a posteriori error estimates. The technology consists of splitting the exact solution into resolved or coarse scales (finite element solution) and unresolved or fine scales (numerical error). By feeding this splitting into the variational formulation, an exact weak form can be derived for the fine scales as a function of the resolved scales. The way of solving or approximating this equation yields different algorithms and models for error estimation. Furthermore, using the so-called fine-scale Green’s function, an analytical representation of the fine scales is possible. Again, different approximations of this function give rise to various algorithms and models. This theory naturally suggests that the error can be computed by the combination of element interior and inter-element faces residuals with the corresponding error time-scales. From this standpoint, error estimators are developed for the transport equation and the Navier–Stokes equations. This technology can be further used for example to generate adapted meshes, to derive reduced order models and in verification and validation algorithms. info:eu-repo/grantAgreement/ES/DGA-FEDER/T32-20R info:eu-repo/grantAgreement/ES/MINECO-AEI-FEDER/PID2019-106099RB-C44 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 6.9 2023 MECHANICS 7 / 170 = 0.041 2023 Q1 T1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 4 / 135 = 0.03 2023 Q1 T1 ENGINEERING, MULTIDISCIPLINARY 6 / 181 = 0.033 2023 Q1 T1 2.397 2023 Computational Mechanics 2023 Q1 Computer Science Applications 2023 Q1 Physics and Astronomy (miscellaneous) 2023 Q1 Mechanics of Materials 2023 Q1 Mechanical Engineering 2023 Q1 12.7 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Irisarri, Diego (orcid)0000-0003-1835-2816 5001 600 Universidad de Zaragoza Dpto. Ciencia Tecnol.Mater.Fl. Área Mecánica de Fluidos 417, Part B (2023), 116341 [36 pp.] Comput. methods appl. mech. eng. Computer Methods in Applied Mechanics and Engineering 0045-7825 2457920 http://zaguan.unizar.es/record/131673/files/texto_completo.pdf Versión publicada 2108092 http://zaguan.unizar.es/record/131673/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:131673 articulos driver 2024-11-22-12:11:48 ARTICLE