A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method

Irisarri, D. (Universidad de Zaragoza) ; Hauke, G. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.cma.2016.09.001

Año: 2016

Publicado en: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 311 (2016), 648-670
ISSN: 0045-7825

Factor impacto JCR: 3.949 (2016)

Categ. JCR: MECHANICS rank: 6 / 133 = 0.045 (2016) - Q1 - T1
Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 3 / 100 = 0.03 (2016) - Q1 - T1
Categ. JCR: ENGINEERING, MULTIDISCIPLINARY rank: 5 / 85 = 0.059 (2016) - Q1 - T1

Factor impacto SCIMAGO: 2.69 - Computational Mechanics (Q1) - Computer Science Applications (Q1) - Physics and Astronomy (miscellaneous) (Q1) - Mechanics of Materials (Q1) - Mechanical Engineering (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/T21
Financiación: info:eu-repo/grantAgreement/ES/MEC/FPU-AP2010-2073
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MAT2013-46467-C4-3-R

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Mecánica de Fluidos (Dpto. Ciencia Tecnol.Mater.Fl.)