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Remarks on mesh quality

Knupp, Patrick K.

Various aspects of mesh quality are surveyed to clarify the disconnect between the traditional uses of mesh quality metrics within industry and the fact that quality ultimately depends on the solution to the physical problem. Truncation error analysis for ffnite difference methods reveals no clear connection to most traditional mesh quality metrics. Finite element bounds to the interpolation error can be shown, in some cases, to be related to known quality metrics such as the condition number. On the other hand, the use of quality metrics that do not take solution characteristics into account can be valid in certain circumstances, primarily as a means of automatically detecting defective meshes. The use of such metrics when applied to simulations for which quality is highly-dependent on the physical solution is clearly inappropriate. Various ffaws and problems with existing quality metrics are mentioned, along with a discussion on the use of threshold values. In closing, the author advocates the investigation of explicitly-referenced quality metrics as a potential means of bridging the gap between a priori quality metrics and solution-dependent metrics.