A node-numbering-invariant directional length scale for simplex elements

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30 Citations (Scopus)


Variational multiscale methods, and their precursors, stabilized methods, have been very popular in flow computations in the past several decades. Stabilization parameters embedded in most of these methods play a significant role. The parameters almost always involve element length scales, most of the time in specific directions, such as the direction of the flow or solution gradient. We require the length scales, including the directional length scales, to have node-numbering invariance for all element types, including simplex elements. We propose a length scale expression meeting that requirement. We analytically evaluate the expression in the context of simplex elements and compared to one of the most widely used length scale expressions and show the levels of noninvariance avoided.

Original languageEnglish
Pages (from-to)2719-2753
Number of pages35
JournalMathematical Models and Methods in Applied Sciences
Issue number14
Publication statusPublished - 2019


  • Stabilization parameter
  • directional element length
  • invariance
  • node-numbering
  • simplex element

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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