Improved error and work estimates for high-order elements

SUMMARY Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements....

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2013-08, Vol.72 (11), p.1207-1218
Main Author: Lohner, Rainald
Format: Article
Language:English
Subjects:
Accuracy
CFD
Computational fluid dynamics
Demand
Errors
Estimates
finite differences
finite elements
Flexibility
high-order schemes
Mathematical analysis
Optimization
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Summary:SUMMARY Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. Copyright © 2013 John Wiley & Sons, Ltd. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of elements in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.3783