An isogeometric collocation method using superconvergent points

Cosmin Anitescu, Yue Jia, Yongjie Jessica Zhang, Timon Rabczuk

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

We develop an IGA collocation method modified by collocating at points other than the standard Greville abscissae. The method is related to orthogonal collocation used for solving differential equations and to the superconvergence theory, therefore we refer to this method as "super-collocation" (IGA-SC). By carefully choosing the collocation points, it can be seen that the IGA-SC converges in the first derivative (energy) norms at rates similar to that of the Galerkin solution. This is different from the collocation at Greville abscissae (IGA-C), where the convergence in energy norm for odd polynomial degrees is typically suboptimal. The method is tested on 1D, 2D and 3D numerical examples, in which it is compared to IGA-C and Galerkin's method (IGA-G). The comparison includes a detailed cost vs. accuracy analysis, which shows an improved efficiency of the proposed method in particular for odd polynomial degrees.

Original languageEnglish
Pages (from-to)1073-1097
Number of pages25
JournalComputer Methods in Applied Mechanics and Engineering
Volume284
DOIs
Publication statusPublished - 2015 Feb 1

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collocation
Polynomials
Galerkin methods
Differential equations
norms
Derivatives
polynomials
Galerkin method
Costs
differential equations
costs
energy

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

An isogeometric collocation method using superconvergent points. / Anitescu, Cosmin; Jia, Yue; Zhang, Yongjie Jessica; Rabczuk, Timon.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 284, 01.02.2015, p. 1073-1097.

Research output: Contribution to journalArticle

Anitescu, Cosmin ; Jia, Yue ; Zhang, Yongjie Jessica ; Rabczuk, Timon. / An isogeometric collocation method using superconvergent points. In: Computer Methods in Applied Mechanics and Engineering. 2015 ; Vol. 284. pp. 1073-1097.
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