Hierarchical Elements, Local Mappings and the $h$-$p$ Version of the Finite Element Method (Ⅰ)

Abstract

This is the first half of an article which develops a theory the hierarchical elements for the $h$-$p$ version of the finite element method in the two-dimensional case. The approximation properties of the hierarchical elements are discussed. The second part will address the convergence rate when geometric meshes are used.