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Moitinho De Almeida, J. P.

A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics. (English) Zbl 1352.74041

Int. J. Numer. Methods Eng. 94, No. 10, 961-984 (2013).
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.

Cited in 13 Documents

MSC:

74B05 Classical linear elasticity
74S05 Finite element methods applied to problems in solid mechanics

Keywords:

error bounds; error estimation; verification; model reduction; proper generalized decomposition; local outputs
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\textit{J. P. Moitinho De Almeida}, Int. J. Numer. Methods Eng. 94, No. 10, 961--984 (2013; Zbl 1352.74041)
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