hp refinement applied to the finite element method should lead to faster convergence than h or prefinement [3,4]. On the other hand, h and p refinements are easier to implement. The complexityof an hp refinement is increased when the process is implemented for any type of mesh [1] In thePZ environment [2], the hp adaptive method was designed to work with heterogeneous mesh.In this paper the implementation of hp adaptivity in the PZ environment will be explained. Thefocus will be on the implementation. The complexity of the code is managed by precisemathematical definition of topological concepts and by their translation in the Object Orientedlanguage C++. hp Adaptivity is implemented in two steps: the geometric element division, whereelement neighboring information is discussed together with the requirement of new nodes creationand the second step where the p-order interpolation space enrichment including restrictionrequirements is discussed. The main result of this research is that a single concept is applicable toall known types of elements. As an extension of this study, a new geometric element division basedon a refinement pattern is presented. A refinement pattern is defined based on an example mesh.Directional refinements are used to illustrate the concept of refinement patterns.The research in hp-adaptivity has evolved from a set of classes which each individuallyimplemented h-refinement to a single templated class where the elements are solely defined basedon their geometry and interpolation functions.
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