Rainald Löhner Improved error and work estimates for high-order elements International Journal for Numerical Methods in Fluids 72
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.
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