Two-dimensional HP-adaptive Algorithm for Continuous Approximations of Material Data Using Space Projection

Piotr Gurgul; Marcin Sieniek; Maciej Paszynski; Lukasz Madej; Nathan Collier

doi:10.7494/csci.2013.14.1.97

Authors

Piotr Gurgul
Marcin Sieniek
Maciej Paszynski
Lukasz Madej
Nathan Collier

DOI:

https://doi.org/10.7494/csci.2013.14.1.97

Keywords:

adaptive ﬁnite element method, projection operator, digital material representation

Abstract

In this paper we utilize the concept of the L2 and H1 projections used toadaptively generate a continuous approximation of an input material data inthe ﬁnite element (FE) base. This approximation, along with a correspondingFE mesh, can be used as material data for FE solvers. We begin with a brieftheoretical background, followed by description of the hp-adaptive algorithmadopted here to improve gradually quality of the projections. We investigatealso a few distinct sample problems, apply the aforementioned algorithms andconclude with numerical results evaluation.

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