000131673 001__ 131673
000131673 005__ 20241125101201.0
000131673 0247_ $$2doi$$a10.1016/j.cma.2023.116341
000131673 0248_ $$2sideral$$a137023
000131673 037__ $$aART-2023-137023
000131673 041__ $$aeng
000131673 100__ $$0(orcid)0000-0001-7802-3411$$aHauke, Guillermo$$uUniversidad de Zaragoza
000131673 245__ $$aA review of VMS a posteriori error estimation with emphasis in fluid mechanics
000131673 260__ $$c2023
000131673 5060_ $$aAccess copy available to the general public$$fUnrestricted
000131673 5203_ $$aThis 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.
000131673 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/T32-20R$$9info:eu-repo/grantAgreement/ES/MINECO-AEI-FEDER/PID2019-106099RB-C44
000131673 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000131673 590__ $$a6.9$$b2023
000131673 592__ $$a2.397$$b2023
000131673 591__ $$aMECHANICS$$b7 / 170 = 0.041$$c2023$$dQ1$$eT1
000131673 593__ $$aComputational Mechanics$$c2023$$dQ1
000131673 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b4 / 135 = 0.03$$c2023$$dQ1$$eT1
000131673 593__ $$aComputer Science Applications$$c2023$$dQ1
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000131673 593__ $$aPhysics and Astronomy (miscellaneous)$$c2023$$dQ1
000131673 593__ $$aMechanics of Materials$$c2023$$dQ1
000131673 593__ $$aMechanical Engineering$$c2023$$dQ1
000131673 594__ $$a12.7$$b2023
000131673 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000131673 700__ $$0(orcid)0000-0003-1835-2816$$aIrisarri, Diego
000131673 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos
000131673 773__ $$g417, Part B (2023), 116341 [36 pp.]$$pComput. methods appl. mech. eng.$$tComputer Methods in Applied Mechanics and Engineering$$x0045-7825
000131673 8564_ $$s2457920$$uhttps://zaguan.unizar.es/record/131673/files/texto_completo.pdf$$yVersión publicada
000131673 8564_ $$s2108092$$uhttps://zaguan.unizar.es/record/131673/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
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000131673 951__ $$a2024-11-22-12:11:48
000131673 980__ $$aARTICLE