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Error analysis and improvement of first‐order design sensitivity relations
Author(s) -
Materna Daniel,
Barthold FranzJoseph
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010284
Subject(s) - sensitivity (control systems) , taylor series , nonlinear system , nonlinear elasticity , representation (politics) , mathematics , error analysis , first order , computer science , mathematical optimization , elasticity (physics) , engineering , mathematical analysis , physics , politics , political science , law , thermodynamics , quantum mechanics , electronic engineering
This contribution is concerned with novel approaches for error estimation and the improvement of first‐order design sensitivities for the state. These approaches are based on an exact representation of the design sensitivity of the state, which is obtained by performing different Taylor expansions with integral remainders. We consider a general variational framework and present the application of the proposed approach to shape sensitivity for the model problem of nonlinear elasticity. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)