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Guaranteed computable bounds for the exact error in the finite element solution—Part II: bounds for the energy norm of the error in two dimensions
Author(s) -
Strouboulis T.,
Babuška I.,
Gangaraj S. K.
Publication year - 2000
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/(sici)1097-0207(20000110/30)47:1/3<427::aid-nme779>3.0.co;2-1
Subject(s) - norm (philosophy) , computation , finite element method , residual , mathematics , exact solutions in general relativity , polygon mesh , upper and lower bounds , element (criminal law) , algorithm , mathematical analysis , geometry , physics , political science , law , thermodynamics
This paper addresses the computation of guaranteed upper and lower bounds for the energy norm of the exact error in the finite element solution. These bounds are constructed in terms of the solutions of local residual problems with equilibrated residual loads and are rather sharp, even for coarse meshes. he sharpness of the bounds can be further improved by employing few iterations of a relatively inexpensive iterative scheme. he main result is that the bounds are guaranteed for the nergy norm of the exact error , unlike the bounds which ave been proposed in [13,14] which are guaranteed only for the nergy norm of the error with respect to an enriched ( truth‐esh ) finite element solution. Copyright © 2000 John Wiley & Sons, Ltd.