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Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

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Volume 61, Issue 1


Application of grid convergence index in FE computation

L. Kwaśniewski
  • Corresponding author
  • Faculty of Civil Engineering, Warsaw University of Technology, 16 Armii Ludowej Ave., 00-637 Warszawa, Poland
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Published Online: 2013-05-01 | DOI: https://doi.org/10.2478/bpasts-2013-0010


This paper presents an application of the grid convergence index (GCI) concept based on the Richardson extrapolation to a selected simple problem of a cantilever beam loaded with vertical forces at the tip end. The GCI method, popular in computational fluid dynamics, has been recently recommended for finite element (FE) applications in solid and structural mechanics. Based on the results obtained usually for three meshes, the GCI method enables one to determine, in an objective manner, the order of convergence to estimate the asymptotic solution and the bounds for discretization error. The example shows that the characteristics of the convergence depend on the selection of the quantity of interest, which can be local or a global functional such as the deflection considered here. The results differ for different FE formulations, and the difference is bigger when the nonlinearities (e.g., due to plastic response) are taken into account

Keywords : discretization error; grid convergence index; finite element; mesh refinement; verification

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About the article

Published Online: 2013-05-01

Published in Print: 2013-03-01

Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences, Volume 61, Issue 1, Pages 123–128, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/bpasts-2013-0010.

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