Improved co‐ordinate transformations for finite elements: The Lagrange cubic case

Michael A. Celia, William G. Gray

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A modified isoparametric co‐ordinate transformation is developed for the case of Lagrange cubic finite elements. This modified transformation produces significant improvements in solution accuracy while eliminating troublesome aspects of the standard isoparametric mapping. In particular, zero Jacobians in the standard transformation, which can occur in elements having non‐uniform node spacing, are completely eliminated with the new transformation. Within the analysis, the range of node locations for which the standard transformation is valid (the Jacobian does not vanish) is determined. The treatment of curved sides is discussed and illustrated. Example calculations using two‐dimensional serendipity elements show that the new transformation provides solutions that are as much as several orders of magnitude more accurate than those computed using the standard formulation.

Original languageEnglish (US)
Pages (from-to)1529-1545
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
StatePublished - Aug 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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