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A‐Posteriori Error Estimation and Adaptivity for the Finite Element Method Using Duality Principles
Author(s) -
Cirak F.,
Ramm E.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19990791337
Subject(s) - duality (order theory) , a priori and a posteriori , dual (grammatical number) , mathematics , estimation , variable (mathematics) , component (thermodynamics) , domain (mathematical analysis) , element (criminal law) , finite element method , mathematical optimization , calculus (dental) , computer science , mathematical analysis , pure mathematics , medicine , art , philosophy , physics , literature , management , epistemology , dentistry , political science , law , economics , thermodynamics
Abstract The present study introduces the concept of error estimation for locally and globally defined variables an structural mechanics. As a basic component of the formulation a dual problem specifically designed for the variables in mind is defined. The influence of the errors of the entire spatial or temporal domain on the local error of the specific variable is filtered out by the corresponding dual (influence) problem. The duality techniques are related to the principle of Betti ‐Maxwell and can be used for error estimation with respect to various locally or globally defined variables.