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Embedding Enriched Partition of Unity Approximations in Finite Element Simulations

: Schweitzer, Marc Alexander; Ziegenhagel, Albert


Griebel, Michael; Schweitzer, Marc Alexander:
Meshfree Methods for Partial Differential Equations VIII
Cham: Springer International Publishing, 2017 (Lecture notes in computational science and engineering 115)
ISBN: 3-319-51953-0
ISBN: 978-3-319-51953-1
ISBN: 978-3-319-51954-8
International Workshop on Meshfree Methods for Partial Differential Equations <8, 2015, Bonn>
Fraunhofer SCAI ()

In this paper we present a general approach to embed arbitrary approximation spaces into classical finite element simulations in a non-intrusive fashion. To this end, we employ a global partition of unity method to splice the two independent approximation spaces together. The main goal of this research is to enable the timely evaluation of novel discretization approaches and meshfree techniques in an industrial context by embedding them into large scale finite element simulations. We present some numerical results showing the generality and effectiveness of our approach.