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

Michael Anthony Celia; William G. Gray

doi:10.1002/nme.1620230809

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

Michael Anthony Celia, William G. Gray

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	1529-1545
Number of pages	17
Journal	International Journal for Numerical Methods in Engineering
Volume	23
Issue number	8
DOIs	https://doi.org/10.1002/nme.1620230809
State	Published - Jan 1 1986
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
Engineering(all)
Applied Mathematics

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10.1002/nme.1620230809

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abstract = "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.",

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N2 - 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.

AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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