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Title: A node-numbering-invariant directional length scale for simplex elements
Authors: Takizawa, K
Ueda, Y 
Tezduyar, TE
Issue Date: 2019
Source: Mathematical models and methods in applied sciences, 1 Nov. 2019, v. 29, no. 14, p. 2719-2753
Abstract: 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.
Keywords: Stabilization parameter
Simplex element
Directional element length
Publisher: World Scientific
Journal: Mathematical models and methods in applied sciences 
ISSN: 0218-2025
EISSN: 1793-6314
DOI: 10.1142/S0218202519500581
Rights: ┬ęThe Author(s)
This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License ( which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
The following publication Takizawa, K., Ueda, Y., & Tezduyar, T. E. (2019). A node-numbering-invariant directional length scale for simplex elements. Mathematical Models and Methods in Applied Sciences, 29(14), 1-35 is available at
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