FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2967507986> ?p ?o ?g. }

• W2967507986 abstract "The present thesis is concerned with a posteriori error estimation for several differential equations of elasticity and fluid mechanics solved by the finite element method.The error estimators are developed in the framework of the variational multiscale theory [1,2], in which the exact solution is split into coarse (or resolved) and fine (or unresolved) scales. In combination with fine-scale Green's functions [3], residual-free bubbles and classic Green's functions, the fine scales are described and their interaction with the coarse scales is established. The error estimation has been accomplished following previous works such as [4,5,6]. According to the nature of the residuals, the error is decomposed in two components: the internal residual error and the inter-element error. In particular, the internal residual error, which has a local character, is modeled with residual-free bubbles or a combination of bubble functions, whereas the inter-element error, which presents a global character, is constituted by classic Green's functions. Using the above model, new explicit and implicit error estimators have been developed. In the literature, we can found a wide number of error estimators both in elasticity and fluid mechanics [7,8,9,10,11]. In this work, global, local and pointwise error estimates have been proposed. The local and global error estimates are constant-free, economical and simple to implement in existing codes. Furthermore, the model yields an accurate pointwise error representation, providing exact pointwise error estimates in one-dimensional problems regardless of the element order. Numerical examples confirm the theoretical framework of this methodology. Adaptive mesh refinement has been carried out allowing to assess the pointwise or elemental error.The error estimation is applied to elasticity for one- and two-dimensional problems [12,13]. For 1D, second and fourth ODEs are considered. In 2D problems, we deal with plane stress problems. As for fluid mechanics, error estimators are proposed for the transport equation and the Stokes equations. Particularly, for the transport equation, the reaction-diffusion and the convection-diffusion equations are considered [14,15]. For the Stokes equations, the error estimation has been carried out for stabilized methods. Implicit and explicit error estimators are presented. Bibliography[1] Hughes, T.: Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput. Meth. Appl. Mech. Engrng. 127, 387–401 (1995)[2] Hughes, T., Feijoo, G., Mazzei, L., Quincy, J.: The variational multiscale method: A paradigm for computational mechanics. Comput. Meth. Appl. Mech. Engrg. 166, 3–24 (1998)[3] Hughes, T., Sangalli, G.: Variational multiscale analysis: the fine-scale Green's function, projection, optimization, localization and stabilized methods. SIAM J. Numer. Anal. 45(2), 539–557 (2007)[4] Hauke, G., Fuster, D., Doweidar, M.H.: Variational multiscale a-posteriori error estimation for the multi-dimensional transport equation. Comput. Meth. Appl. Mech. Engrg. 197, 2701–2718 (2008)[5] Hauke, G., Doweidar, M.H., Miana, M.: Proper intrinsic scales for a-posteriori multiscale error estimation. Comput. Meth. Appl. Mech. Engrng 195, 3983–4001 (2006)[6] Hauke, G., Irisarri, D., Lizarraga, F., et al.: Recent advances on explicit variational multiscale a posteriori error estimation for systems. International Journal of Numerical Analysis and Modeling 11(2), 372–384 (2014)[7] Ainsworth, M., Oden, J.T.: A posterior error estimation in finite element analysis. John Wiley & Sons (2000)[8] Babuska, I., Strouboulis, T.: The finite element method and its reliability. Oxford university press (2001)[9] Diez, P., Pares, N., Huerta, A.: Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates. International Journal for Numerical Methods in Engineering 56(10), 1465–1488 (2003)[10] Ladeveze, P., Leguillon, D.: Error estimate procedure in the finite element method and applications. SIAM J. Numer. Anal. 20, 485–509 (1983)[11] Zienkiewicz, O.C., Zhu, J.Z.: A simple error estimator in the finite element method. Int. J. Numer. Methods Engrg 24, 337–357. (1987)[12] Irisarri, D., Hauke, G.: Variational multiscale a posteriori error estimation for 2nd and 4th-order ODEs. International Journal of Numerical Analysis & Modeling 12(3) (2015)[13] Hauke, G., Irisarri, D.: Variational multiscale a posteriori error estimation for systems. Application to linear elasticity. Computer Methods in Applied Mechanics and Engineering 285, 291–314 (2015)[14] Irisarri, D., Hauke, G.: Pointwise error estimation for the one-dimensional transport equation based on the variational multiscale method. International Journal of Computational Methods p. To appear (2016). DOI 10.1142/S0219876217500402.[15] Irisarri, D., Hauke, G.: A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method. Computer Methods in Applied Mechanics and Engineering 311, 648–670 (2016)" @default.
• W2967507986 created "2019-08-22" @default.
• W2967507986 creator A5083870213 @default.
• W2967507986 date "2017-01-01" @default.
• W2967507986 modified "2023-09-24" @default.
• W2967507986 title "Variational multiscale a posteriori error estimation in finite element methods for fluid mechanics and elasticity" @default.
• W2967507986 hasPublicationYear "2017" @default.
• W2967507986 type Work @default.
• W2967507986 sameAs 2967507986 @default.
• W2967507986 citedByCount "0" @default.
• W2967507986 crossrefType "journal-article" @default.
• W2967507986 hasAuthorship W2967507986A5083870213 @default.
• W2967507986 hasConcept C105795698 @default.
• W2967507986 hasConcept C111472728 @default.
• W2967507986 hasConcept C11413529 @default.
• W2967507986 hasConcept C121332964 @default.
• W2967507986 hasConcept C121854251 @default.
• W2967507986 hasConcept C122383733 @default.
• W2967507986 hasConcept C123614077 @default.
• W2967507986 hasConcept C126255220 @default.
• W2967507986 hasConcept C134306372 @default.
• W2967507986 hasConcept C135628077 @default.
• W2967507986 hasConcept C138885662 @default.
• W2967507986 hasConcept C155512373 @default.
• W2967507986 hasConcept C159674985 @default.
• W2967507986 hasConcept C185429906 @default.
• W2967507986 hasConcept C186899397 @default.
• W2967507986 hasConcept C2777984123 @default.
• W2967507986 hasConcept C28826006 @default.
• W2967507986 hasConcept C33923547 @default.
• W2967507986 hasConcept C75553542 @default.
• W2967507986 hasConcept C97355855 @default.
• W2967507986 hasConceptScore W2967507986C105795698 @default.
• W2967507986 hasConceptScore W2967507986C111472728 @default.
• W2967507986 hasConceptScore W2967507986C11413529 @default.
• W2967507986 hasConceptScore W2967507986C121332964 @default.
• W2967507986 hasConceptScore W2967507986C121854251 @default.
• W2967507986 hasConceptScore W2967507986C122383733 @default.
• W2967507986 hasConceptScore W2967507986C123614077 @default.
• W2967507986 hasConceptScore W2967507986C126255220 @default.
• W2967507986 hasConceptScore W2967507986C134306372 @default.
• W2967507986 hasConceptScore W2967507986C135628077 @default.
• W2967507986 hasConceptScore W2967507986C138885662 @default.
• W2967507986 hasConceptScore W2967507986C155512373 @default.
• W2967507986 hasConceptScore W2967507986C159674985 @default.
• W2967507986 hasConceptScore W2967507986C185429906 @default.
• W2967507986 hasConceptScore W2967507986C186899397 @default.
• W2967507986 hasConceptScore W2967507986C2777984123 @default.
• W2967507986 hasConceptScore W2967507986C28826006 @default.
• W2967507986 hasConceptScore W2967507986C33923547 @default.
• W2967507986 hasConceptScore W2967507986C75553542 @default.
• W2967507986 hasConceptScore W2967507986C97355855 @default.
• W2967507986 hasLocation W29675079861 @default.
• W2967507986 hasOpenAccess W2967507986 @default.
• W2967507986 hasPrimaryLocation W29675079861 @default.
• W2967507986 hasRelatedWork W110622454 @default.
• W2967507986 hasRelatedWork W147539326 @default.
• W2967507986 hasRelatedWork W1533740520 @default.
• W2967507986 hasRelatedWork W1969124885 @default.
• W2967507986 hasRelatedWork W1986296604 @default.
• W2967507986 hasRelatedWork W1996795707 @default.
• W2967507986 hasRelatedWork W2004434601 @default.
• W2967507986 hasRelatedWork W2010271936 @default.
• W2967507986 hasRelatedWork W2031649670 @default.
• W2967507986 hasRelatedWork W2040367551 @default.
• W2967507986 hasRelatedWork W2056244860 @default.
• W2967507986 hasRelatedWork W2135855856 @default.
• W2967507986 hasRelatedWork W2137365186 @default.
• W2967507986 hasRelatedWork W2154953812 @default.
• W2967507986 hasRelatedWork W2170429437 @default.
• W2967507986 hasRelatedWork W2170548731 @default.
• W2967507986 hasRelatedWork W2241009094 @default.
• W2967507986 hasRelatedWork W2894415323 @default.
• W2967507986 hasRelatedWork W2969391195 @default.
• W2967507986 hasRelatedWork W2189142444 @default.
• W2967507986 isParatext "false" @default.
• W2967507986 isRetracted "false" @default.
• W2967507986 magId "2967507986" @default.
• W2967507986 workType "article" @default.