An adaptive h-hierarchical finite element system

A significant amount of computational mechanics research effort in recent years has concentrated on automation of the finite element method. The goal is to achieve a finite element system to which the engineer need only specify the problem geometry, material properties and boundary conditions, together with an indicator of the desired level of accuracy. A finite element model of the problem is then formed, and automatically refined until the specified level of accuracy is achieved. One method of refinement is the h-hierarchical method, in which an initial element mesh is progressively subdivided. However, examples of this type of refinement available in the literature use only quadrilateral or only triangular elements. This paper presents a scheme that allows elements with varying numbers of faces to be used together in an adaptive h-hierarchical analysis. The complexity that would normally be involved in such an approach is controlled by using object oriented techniques. Examples are presented illustrating the utility of the method.