A hierarchical finite element method based on the partition of unity Original Research Article

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 C0 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.