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  • We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary dimension. The estimator provides a guaranteed upper bound on the energy norm of the error and it is robust for all values of the reaction coefficient, including the singularly perturbed case. The approach is based on robustly equilibrated boundary flux functions of Ainsworth and Oden (2000) and on subsequent robust and explicit flux reconstruction. This paper simplifies and extends the applicability of the previous result of Ainsworth and Vejchodsky (2011) in three aspects: (i) arbitrary dimension, (ii) mixed boundary conditions, and (iii) non-constant reaction coefficient. It is the first robust upper bound on the error with these properties.
  • We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary dimension. The estimator provides a guaranteed upper bound on the energy norm of the error and it is robust for all values of the reaction coefficient, including the singularly perturbed case. The approach is based on robustly equilibrated boundary flux functions of Ainsworth and Oden (2000) and on subsequent robust and explicit flux reconstruction. This paper simplifies and extends the applicability of the previous result of Ainsworth and Vejchodsky (2011) in three aspects: (i) arbitrary dimension, (ii) mixed boundary conditions, and (iii) non-constant reaction coefficient. It is the first robust upper bound on the error with these properties. (en)
Title
  • Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension
  • Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension (en)
skos:prefLabel
  • Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension
  • Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension (en)
skos:notation
  • RIV/67985840:_____/14:00431616!RIV15-AV0-67985840
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • I
http://linked.open...iv/cisloPeriodika
  • November 2014
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  • 42966
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  • RIV/67985840:_____/14:00431616
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  • finite element analysis; a posteriori error estimate; singularly perturbed problems (en)
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  • CH - Švýcarská konfederace
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  • [9F0083F79605]
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  • Computer Methods in Applied Mechanics and Engineering
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  • 281
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  • Ainsworth, M.
  • Vejchodský, Tomáš
http://linked.open...ain/vavai/riv/wos
  • 000343841400008
issn
  • 0045-7825
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.cma.2014.08.005
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