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A posteriori pointwise upper bound error estimates in the finite element method
Author(s) -
Yang J. D.,
Kelly D. W.,
Isles J. D.
Publication year - 1993
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.1620360803
Subject(s) - pointwise , finite element method , upper and lower bounds , mathematics , bilinear interpolation , residual , mixed finite element method , finite element limit analysis , mathematical analysis , algorithm , statistics , structural engineering , engineering
An error estimate for the finite element method is presented in this paper. The error is identified as the response to a set of residual forces, and a complementary analysis provides an upper bound estimate of the global energy of the error. The inequality proposed by Babuška and Miller 1 is then employed to bound the error in stress and displacement at a point. The formula is derived for two‐dimensional elasticity, but the procedure is general; and can be applied to three‐dimensional and other problems. Numerical experiments using the procedure are carried out and the results are given for the four‐node bilinear compatible element and plane stress.