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A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics
Author(s) -
Almeida J. P. Moitinho
Publication year - 2013
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.4490
Subject(s) - bounding overwatch , convergence (economics) , decomposition , mathematics , parametric statistics , basis (linear algebra) , simple (philosophy) , mathematical optimization , solid mechanics , computer science , geometry , statistics , artificial intelligence , physics , thermodynamics , ecology , philosophy , epistemology , economics , biology , economic growth
SUMMARY This paper presents an approach that extends the classical error bounding techniques to parametric models. It departs from appropriate pairs of complementary solutions of a linear elastic problem, obtained using a Proper Generalised Decomposition methodology, to determine approximations of selected local outputs and strict bounds of the error of these approximations. The paper starts by presenting the procedures used to obtain the complementary solutions. The properties, the convergence characteristics of the global error and the determination of an indicator of the error distribution are illustrated for a very simple example. The demonstration of the procedure used for determining local outputs and their bounds, also accompanied by illustrative examples, completes the paper.Copyright © 2013 John Wiley & Sons, Ltd.