Distortion, degeneracy and rezoning in finite elements - A survey

The results obtained from finite element analysis are significantly affected by the quality of elements. In certain applications like shape optimization, crash analysis, metal forming, fluid flow analysis, and large displacement analysis, the finite element mesh is systematically updated in an iterative process. In such situations, in spite of an ideal starting mesh, the quality of elements could deteriorate, causing severly distorted elements. In extreme cases, the elements become degenerate and further progress of analysis is restricted. An understanding of the methods of quantifying element distortion helps in identifying 'bad' geometry and in deciding when to remesh. Knowledge about geometric configurations which cause degeneracy assists in controlling degeneracy during the analysis. This paper contains a survey of available distortion measures and degeneracy conditions for various elements in two and three dimensions. It is a review of the literature in this field in the last two decades. A brief review of rezoning is also included, since it is one of the more popularly used methods to correct a distorted mesh.