Flexible piecewise approximations based on partition of unity

Weimin Han, Wing Kam Liu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.

Original languageEnglish (US)
Pages (from-to)191-199
Number of pages9
JournalAdvances in Computational Mathematics
Issue number1-2
StatePublished - Jul 2005


  • Galerkin method
  • Nodal interpolation
  • Partition of unity
  • Polynomial reproducing
  • Smooth piecewise approximation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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