Higher-Order Accurate Integration for Cut Elements with Chen-Babuška Nodes

  • Thomas-Peter FriesEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 12)


The higher-order accurate numerical integration of geometries that are implicitly defined by level-set functions is considered. A higher-order background mesh is employed providing an interpolation of the level-set function by Lagrangian shape functions. The integration may take place on the zero-level set or in the domains defined by the sign of the level-set function. This work is a follow-up of Fries and Omerović (Int J Numer Methods Eng, doi:10.1002/nme.5121). Herein, it is shown that special distributions of the element nodes, which are optimized for integration, yield significantly better results than equally-spaced nodes. Different error norms are proposed which allow to investigate the accuracy of general implicit geometries in two and three dimensions.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Structural AnalysisGraz University of TechnologyGrazAustria

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