Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis

Dominik Schillinger, Shaikh J. Hossain, Thomas J.R. Hughes

Research output: Contribution to journalArticlepeer-review

95 Scopus citations


We explore the use of various element-based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis. The rules studied encompass tensor-product Gauss and Gauss-Lobatto rules, and certain so-called monomial rules that do no possess a tensor-product structure. The objective of the study is to determine quadrature strategies, which enjoy the same accuracy and stability behavior as full Gauss quadrature, but with significantly fewer quadrature points. Several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard b C 0-continuous finite elements of the same order.

Original languageEnglish (US)
Pages (from-to)1-45
Number of pages45
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Aug 1 2014

Bibliographical note

Funding Information:
D. Schillinger, S.J. Hossain and T.J.R. Hughes were supported by grants from the Office of Naval Research ( N00014-08-1-0992 ) and the National Science Foundation ( CMMI-01101007 ), with the University of Texas at Austin. D. Schillinger was also supported by the German Research Foundation (Deutsche Forschungsgemeinschaft DFG) under grant SCHI 1249/1-2 . The authors wish to thank C.A. Felippa for his input that motivated the study of Felippa’s rule.


  • Gauss-Lobatto integration
  • Isogeometric analysis
  • Monomial quadrature rules
  • Reduced quadrature rules

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