A priori error estimations of hp-finite element approximations for hierarchical models of plate- and shell-like structures

Abstract

A priori error estimates of hp-finite element approximations for hierarchical models of the thin elastic plate- and shell-like structures are derived. The error in the approximations of a hierarchical model consists of the modelling error due to assumptions on displacement or stress fields and the finite element approximation error of discretizations of such a model. Also, non-uniformity with respect to the thickness owing to numerical locking is included in the present error estimates. Numerical results are given supporting the theoretical results.