Recent Developments In Basic Finite Element Technologies

Abstract

High performance (HP) elements are simple finite elements constructed to deliver engineering accuracy with arbitrary coarse meshes. This paper overviews original developments based on parametrized variational principles, which provide a common foundation for various approaches to HP element construction. This work led to the template approach. Templates are parametrized algebraic forms of finite element stiffness equations. The application of templates to the construction of an optimal 3-node plate bending element is outlined. The template approach holds future promise in the unification of finite element methods and connection to arbitrary grid finite differences. Essential to this unification work is the availability of powerful computer algebra systems.