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Abstract: This is the second paper out of a series of papers devoted to model- and hpq-adaptive finite element methods assigned for the modeling and analysis of elastic structures of complex mechanical description. In our previous publication we investigated the issue of hierarchical models and approximations of such structures. We applied 3D or 3D-based mechanical models, hierarchical modeling, and hierarchical approximations within the proposed finite element formulation. Furthermore, we assumed that the mechanical model and discretization parameters (such as: the size h of the element, and the longitudinal and transverse approximation orders, p and q) could vary locally, i.e. they could be different in each finite element. The a posteriori error estimation discussed in the present paper is based on the generalization of the residual equilibration method on the models with internal constraints. The generalized method is applied to the assessment of the total and approximation errors, while the modeling error is calculated as the difference between the former two errors. The corresponding error-controlled adaptive procedures are based on a three-step strategy, with possible iterations of h- and p-steps. [Copyright &y& Elsevier]

Abstract: This is a paper out of a series of three papers devoted to model- and hpq-adaptive finite element methods assigned for modeling and analysis of complex structures. In this paper we focus our attention on hierarchical models and hierarchical approximations, while the issues of error estimation and adaptivity control will be presented in the next papers of the series. In all the papers we consider the elastic structures of complex mechanical description. We apply 3D or 3D-based mechanical models, hierarchical modeling, and hierarchical approximations within our finite element formulation. In the proposed approach, the mechanical model and discretization parameters, such as the size h of the element, and the longitudinal and transverse approximation orders, p and q, can vary locally, i.e. they can be different in each finite element. The a posteriori error estimation is based on the residual equilibration methods applied to the assessment of the modeling and approximation errors. The error-controlled adaptive procedures are derived from a four-step strategy, with possible iterations on h- and p-steps. [ABSTRACT FROM AUTHOR]