60915 20200221144257.0 doi 10.1016/j.cma.2016.09.001 sideral 96743 ART-2016-96743 eng (orcid)0000-0003-1835-2816 Irisarri, D. Universidad de Zaragoza A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method 2016 Access copy available to the general public Unrestricted This 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. info:eu-repo/grantAgreement/ES/DGA/T21 info:eu-repo/grantAgreement/ES/MEC/FPU-AP2010-2073 info:eu-repo/grantAgreement/ES/MINECO/MAT2013-46467-C4-3-R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 3.949 2016 MECHANICS 6 / 133 = 0.045 2016 Q1 T1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 3 / 100 = 0.03 2016 Q1 T1 ENGINEERING, MULTIDISCIPLINARY 5 / 85 = 0.059 2016 Q1 T1 2.69 2016 Computational Mechanics 2016 Q1 Computer Science Applications 2016 Q1 Physics and Astronomy (miscellaneous) 2016 Q1 Mechanics of Materials 2016 Q1 Mechanical Engineering 2016 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0001-7802-3411 Hauke, G. Universidad de Zaragoza 5001 600 Universidad de Zaragoza Dpto. Ciencia Tecnol.Mater.Fl. Área Mecánica de Fluidos 311 (2016), 648-670 Comput. methods appl. mech. eng. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 0045-7825 1634302 http://zaguan.unizar.es/record/60915/files/texto_completo.pdf Postprint 64878 http://zaguan.unizar.es/record/60915/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:60915 articulos driver 2020-02-21-13:30:13 ARTICLE