A Higher Order Isoparametric Fictitious Domain Method for Level Set Domains

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 121)

Abstract

We consider a new fictitious domain approach of higher order accuracy. To implement Dirichlet conditions we apply the classical Nitsche method combined with a facet-based stabilization (ghost penalty). Both techniques are combined with a higher order isoparametric finite element space which is based on a special mesh transformation. The mesh transformation is build upon a higher order accurate level set representation and allows to reduce the problem of numerical integration to problems on domains which are described by piecewise linear level set functions. The combination of this strategy for the numerical integration and the stabilized Nitsche formulation results in an accurate and robust method. We introduce and analyze it and give numerical examples.

Notes

Acknowledgements

The author gratefully acknowledges funding by the German Science Foundation (DFG) within the project “LE 3726/1-1”.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Georg-August-Universität GöttingenInstitut für Numerische und Angewandte MathematikGöttingenGermany

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