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Title:
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Probabilistic analysis of an a posteriori error estimator for finite elements
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Author:
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Díez, Pedro; Egozcue Rubí, Juan José
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
-Finite element method
-Errors--Mathematical models
-Error estimation
-probabilistic analysis
-finite elements
-adaptivity
-Elements finits, Mètode dels
-Anàlisi d'error (Matemàtica) |
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Rights:
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Document type:
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Article - Submitted version
Article |
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