Probabilistic analysis of an a posteriori error estimator for finite elements

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/8549

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor	Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística
dc.contributor	Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.contributor.author	Díez, Pedro
dc.contributor.author	Egozcue Rubí, Juan José
dc.date	2001-08
dc.identifier.citation	Díez, P.; Egozcue, J. J. Probabilistic analysis of an a posteriori error estimator for finite elements. "Mathematical models and methods in applied sciences", Agost 2001, vol. 11, núm. 5, Electronic version of an article published as [Mathematical models and methods in applied sciences , 11, 5, 2001, 841-854] [10.1142/S0218202501001136 ] © [copyright World Scientific Publishing Company] [http://journals.worldscientific.com.sg/m3as/], p. 841-854.
dc.identifier.citation	0218-2025
dc.identifier.citation	10.1142/S0218202501001136
dc.identifier.uri	http://hdl.handle.net/2117/8549
dc.language.iso	eng
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
dc.subject	Finite element method
dc.subject	Errors--Mathematical models
dc.subject	Error estimation
dc.subject	probabilistic analysis
dc.subject	finite elements
dc.subject	adaptivity
dc.subject	Elements finits, Mètode dels
dc.subject	Anàlisi d'error (Matemàtica)
dc.title	Probabilistic analysis of an a posteriori error estimator for finite elements
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	A residual type a posteriori error estimator for finite elements is analyzed using a new technique. In this case, the error estimate is the result of two consecutive projections of the exact error on two finite-dimensional subspaces. The analysis introduced in this paper is based on a probabilistic approach, that is, the idea is to assess the average value of the effectivity index (the ratio estimated error over exact error) by assuming the randomness of the exact error. The average value characterizes the mean behavior of the estimator and it is found to be related with some geometric properties of the subspaces. These geometric properties are obtained from the standard matrices of the linear systems arising in the formulation of the finite element method.
dc.description.abstract	Peer Reviewed

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