Two-dimensional hp-adaptive algorithm for continuous approximations of material data using space projection

Abstract

In this paper we utilize the concept of the $L^2$ and $H^1$ projections used to adaptively generate a continuous approximation of an input material data in the finie element (FE) base.This approximation, along with a corresponding FE mesh, can be used as material data for FE solvers. We begin with abrief theoretical background, followed by description of the hp -adaptive algorithm adopted here to improve gradually quality of the projections. We investigate also a few distinct sample problems, apply the aforementioned algorithms and conclude with numerical results evaluation.