Abstract2018-05-24T12:52:58+00:00

Un estimador de error residual semiexplícito en cantidades de interés para un problema mecánico lineal

Author (s): Rosales, R. and Díez, P.
Journal: Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería

Volume: 32, Issue 4
Pages: 212 – 220
Date: 2015

Abstract:
We aim at defining a semi-explicit approach to estimate the error in quantities of interest associated
with the Finite Element solution of a linear elasticity problem. The advocated procedure is split in two
parts, an implicit error estimate for the adjoint problem and an explicit estimate assessing the error
in the direct (primal) problem. The implicit part of the estimate (on the adjoint problem) embraces two
phases, each consisting in projecting the error on “bubble” functional spaces. The projections are low-cost
operations due to their local nature. The two phases account the error in the interior of the elements and
the contribution of the elementary edges (associated with the tractions jump). The implicit character of
this part is provided by the solution of the local problems in low-dimensional functional spaces. We also
analyze the particular case of selecting one-dimensionalfunctional spaces (setting the shape ofthe bubble
and computing a scalar coefficient), which, in practice, make this part of the process explicit. The explicit
part of the estimate consists in injecting in the weak primal residual the approximation of the adjoint
error obtained in the first phase. This approach is similar to the DWR method but using a weak formulation
of the residual and injecting an implicitly estimated adjoint error rather than a post-processed solution.
The proposed methodology is validated in a numerical example.

  
  

Bibtex:

@article{Rosales2016212,
title = "Un estimador de error residual semiexplícito en cantidades de interés para un problema mecánico lineal ",
journal = "Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería ",
volume = "32",
number = "4",
pages = "212 - 220",
year = "2016",
note = "",
issn = "0213-1315",
doi = "http://dx.doi.org/10.1016/j.rimni.2015.06.001",
url = "http://www.sciencedirect.com/science/article/pii/S0213131515000504",
author = "R. Rosales and P. Díez",
keywords = "Estimación del error",
keywords = "Semiexplícita",
keywords = "Funciones burbuja",
keywords = "Estimadores residuales",
keywords = "Error estimation",
keywords = "Semi-explicit",
keywords = "Bubble functional spaces",
keywords = "Residual estimates "
}