A residual a posteriori error estimate for partition of unity finite elements for three-dimensional transient heat diffusion problems using multiple global enrichment functions

Muhammad Iqbal*, Heiko Gimperlein, Omar Laghrouche, Khurshid Alam, M. Shadi Mohamed, Muhammad Abid

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


In this article, a study of residual based a posteriori error estimation is presented for the partition of unity finite element method (PUFEM) for three-dimensional (3D) transient heat diffusion problems. The proposed error estimate is independent of the heuristically selected enrichment functions and provides a useful and reliable upper bound for the discretization errors of the PUFEM solutions. Numerical results show that the presented error estimate efficiently captures the effect of h-refinement and q-refinement on the performance of PUFEM solutions. It also efficiently reflects the effect of ill-conditioning of the stiffness matrix that is typically experienced in the partition of unity based finite element methods. For a problem with a known exact solution, the error estimate is shown to capture the same solution trends as obtained by the classical L2 norm error. For problems with no known analytical solutions, the proposed estimate is shown to be used as a reliable and efficient tool to predict the numerical errors in the PUFEM solutions of 3D transient heat diffusion problems.

Original languageEnglish
Pages (from-to)2727-2746
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number12
Publication statusPublished - Jun 30 2020
Externally publishedYes


  • diffusion problems
  • enrichment functions
  • error estimate
  • GFEM

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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