A hierarchical finite element method based on the partition of unity

Published in Comput. Methods Appl. Mech. Engrg., Vol. 152, pp. 73-84, 1998
doi: 10.1016/S0045-7825(97)00182-5

Abstract

In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added to base finite element interpolations which, for Co approximations, are a particular case of the partition of unity. We also show how the functions may be constructed to preserve the interpolation property of the base finite element functions. An application to linear elasticity is used to illustrate the properties and stability of the approximation.