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Modeling error and adapticity in nonlinear continuum mechanics. (English) Zbl 1012.74081

Summary: We derive computable global bounds on errors due to the use of various mathematical models of physical phenomena. The procedure involves identifying the so-called fine model among a class of models of certain events, and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modelling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics.

MSC:

74S99 Numerical and other methods in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
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