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Element by element a posteriori error estimation and improvement of stress solutions for two‐dimensional elastic problems
Author(s) -
Ohtsubo Hideomi,
Kitamura Mitsuru
Publication year - 1990
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.1620290202
Subject(s) - finite element method , mixed finite element method , smoothed finite element method , extended finite element method , finite element limit analysis , a priori and a posteriori , element (criminal law) , computation , mathematics , node (physics) , linear elasticity , hp fem , boundary knot method , algorithm , computer science , mathematical optimization , structural engineering , engineering , boundary element method , philosophy , epistemology , political science , law
A quantitative method of a posteriori error estimation based on finite element solutions is developed. The proposed method can estimate the error of solutions obtained by the finite element method for two‐dimensional elastic problems with 4‐node elements. Since the error is estimated element by element, the proposed method does not require a large memory or long computing time. Not only rectangular elements but also arbitrarily shaped 4‐node elements can be used in this method for estimating the error in the finite element computation with high accuracy. The finite element solutions are improved by adding the estimated errors onto the original solutions. The proposed method can be utilized for any type of linear problem if an isoparametric finite element method is used.