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Guaranteed error bounds on pointwise quantities of interest for transient viscodynamics problems

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Abstract

A new method is developed to obtain guaranteed error bounds on pointwise quantities of interest for linear transient viscodynamics problems. The calculation of strict error bounds is based on the concept of “constitutive relation error” (CRE) and the solution of an adjoint problem. The central and original point of this work is the treatment of the singularity in space and time introduced by the loading of the adjoint problem. Hence, the adjoint solution is decomposed into two parts: (i) an analytical part determined from Green’s functions; (ii) a residual part approximated with classical numerical tools (finite element method, Newmark integration scheme). The capabilities and the limits of the proposed approach are analyzed on a 2D example.

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Authors and Affiliations

  1. LMT-Cachan (ENS-Cachan/CNRS/UPMC/PRES UniverSud Paris), 61 avenue du Président Wilson, 94235, Cachan Cedex, France

    Julien Waeytens, Ludovic Chamoin & Pierre Ladevéze

Authors
  1. Julien Waeytens
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  2. Ludovic Chamoin
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  3. Pierre Ladevéze
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Correspondence to Pierre Ladevéze.

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Waeytens, J., Chamoin, L. & Ladevéze, P. Guaranteed error bounds on pointwise quantities of interest for transient viscodynamics problems. Comput Mech 49, 291–307 (2012). https://doi.org/10.1007/s00466-011-0642-1

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  • DOI: https://doi.org/10.1007/s00466-011-0642-1

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