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Element by element a posteriori error estimation of the finite element analysis for three‐dimensional elastic problems
Author(s) -
Ohtsubo Hideomi,
Kitamura Mitsuru
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330813
Subject(s) - finite element method , mixed finite element method , extended finite element method , finite element limit analysis , hexahedron , smoothed finite element method , interpolation (computer graphics) , mathematics , a priori and a posteriori , element (criminal law) , hp fem , discontinuity (linguistics) , spectral element method , mathematical optimization , mathematical analysis , boundary knot method , computer science , structural engineering , boundary element method , engineering , animation , philosophy , computer graphics (images) , epistemology , law , political science
An a posteriori error estimation method for finite element solutions for three‐dimensional elastic problems is presented based on the theory developed by the authors for two‐dimensional problems. 1 The error is estimated for the finite element solutions obtained using three‐dimensional 8‐node elements with a linear interpolation function in an arbitrary hexahedron. The method is successfully applied to three‐dimensional elastic problems. In order to decrease computing time and memory use, the error is estimated element by element. The major difficulty in the element‐wise error estimation technique is satisfying the self‐equilibrium condition of applied forces, especially in three‐dimensional problems. These forces are mainly due to traction discontinuity on the element boundaries. The difficulty is circumvented by employing an element‐wise optimal procedure. It is also shown that a very accurate stress solution can be obtained by adding estimated error to the original finite element solutions.