A posteriori error estimator for hierarchical models for elastic bodies with thin domain

A concept of hierarchical modeling, the newest modeling technology, has bee n introduced in early 1990's. This new technology has a great potential to advance the capabilities of current computational mechanics. A first step t o implement this concept is to construct hierarchical models, a family of m athematical models sequentially connected by a key parameter of the problem under consideration and have different levels in modeling accuracy, and to investigate characteristics in their numerical simulation aspects. Among r epresentative model problems to explore this concept are elastic structures such as beam-, arch-, plate- and shell-like structures because the mechani cal behavior through the thickness can be approximated with sequential accu racy by varying the order of thickness polynomials in the displacement or s tress fields. But, in the numerical, analysis of hierarchical models, two k inds of errors prevail, the modeling error and the numerical approximation error. To ensure numerical simulation quality, an accurate estimation of th ese two errors is definitely essential. Here, a local a posteriori error es timator for elastic structures with thin domain such as plate- and shell-li ke structures is derived using the element residuals and the flux balancing technique. This method guarantees upper bounds for the global error, and a lso provides accurate local error indicators for two types of errors, in th e energy norm. Compared to the classical error estimators using the flux av eraging technique, this shows considerably reliable and accurate effectivit y indices. To illustrate the theoretical results and to verify the validity of the proposed error estimator, representative numerical examples are pro vided.