Adaptive hpq-finite element methods of hierarchical models for plate- and shell-like structures

Abstract

A four-step adaptive strategy for hpq-finite element approximations of hierarchical models of the thin plate- and shell-like structures is derived based on a priori and a posteriori error estimations. This strategy controls three parameters; the model level q, the mesh size h, and the approximation order p so as to produce quasi-optimal hierarchical models and finite element meshes. Numerical results are given supporting the theoretical results.