000060915 001__ 60915
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000060915 0247_ $$2doi$$a10.1016/j.cma.2016.09.001
000060915 0248_ $$2sideral$$a96743
000060915 037__ $$aART-2016-96743
000060915 041__ $$aeng
000060915 100__ $$0(orcid)0000-0003-1835-2816$$aIrisarri, D.$$uUniversidad de Zaragoza
000060915 245__ $$aA posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method
000060915 260__ $$c2016
000060915 5060_ $$aAccess copy available to the general public$$fUnrestricted
000060915 5203_ $$aThis article presents a general framework to estimate the pointwise error of linear partial differential equations. The error estimator is based on the variational multiscale theory, in which the error is decomposed in two components according to the nature of the residuals: element interior residuals and inter-element jumps. The relationship between the residuals (coarse scales) and the error components (fine scales) is established, yielding to a very simple model. In particular, the pointwise error is modeled as a linear combination of bubble functions and Green’s functions. If residual-free bubbles and the classical Green’s function are employed, the technology leads to an exact explicit method for the pointwise error. If bubble functions and free-space Green’s functions are employed, then a local projection problem must be solved within each element and a global boundary integral equation must be solved on the domain boundary. As a consequence, this gives a model for the so-called fine-scale Green’s functions. The numerical error is studied for the standard Galerkin and SUPG methods with application to the heat equation, the reaction–diffusion equation and the convection–diffusion equation. Numerical results show that stabilized methods minimize the propagation of pollution errors, which stay mostly locally.
000060915 536__ $$9info:eu-repo/grantAgreement/ES/DGA/T21$$9info:eu-repo/grantAgreement/ES/MEC/FPU-AP2010-2073$$9info:eu-repo/grantAgreement/ES/MINECO/MAT2013-46467-C4-3-R
000060915 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000060915 590__ $$a3.949$$b2016
000060915 591__ $$aMECHANICS$$b6 / 133 = 0.045$$c2016$$dQ1$$eT1
000060915 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b3 / 100 = 0.03$$c2016$$dQ1$$eT1
000060915 591__ $$aENGINEERING, MULTIDISCIPLINARY$$b5 / 85 = 0.059$$c2016$$dQ1$$eT1
000060915 592__ $$a2.69$$b2016
000060915 593__ $$aComputational Mechanics$$c2016$$dQ1
000060915 593__ $$aComputer Science Applications$$c2016$$dQ1
000060915 593__ $$aPhysics and Astronomy (miscellaneous)$$c2016$$dQ1
000060915 593__ $$aMechanics of Materials$$c2016$$dQ1
000060915 593__ $$aMechanical Engineering$$c2016$$dQ1
000060915 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000060915 700__ $$0(orcid)0000-0001-7802-3411$$aHauke, G.$$uUniversidad de Zaragoza
000060915 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos
000060915 773__ $$g311 (2016), 648-670$$pComput. methods appl. mech. eng.$$tCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING$$x0045-7825
000060915 8564_ $$s1634302$$uhttps://zaguan.unizar.es/record/60915/files/texto_completo.pdf$$yPostprint
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000060915 951__ $$a2020-02-21-13:30:13
000060915 980__ $$aARTICLE