The intrinsic partition of unity method

Thomas Peter Fries*, Ted Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A method is presented which enables the global enrichment of the approximation space without introducing additional unknowns. Only one shape function per node is used. The shape functions are constructed by means of the moving least-squares method with an intrinsic basis vector and weight functions based on finite element shape functions. The enrichment is achieved through the intrinsic basis. By using polynomials in the intrinsic basis, optimal rates of convergence can be achieved even on distorted elements. Special enrichment functions can be chosen to enhance accuracy for solutions that are not polynomial in character. Results are presented which show optimal convergence on randomly distorted elements and improved accuracy for the oscillatory solution of the Helmholtz equation.

Original languageEnglish
Pages (from-to)803-814
Number of pages12
JournalComputational Mechanics
Issue number4
Publication statusPublished - Sept 2007

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality


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