An Introduction to Mesh Quality

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to finite element methods is used to understand the basis of present-day geometrical mesh quality indicators. Simple tetrahedral mesh quality measures using both geometrical and solution information are described. Some of the issues in mesh quality for unstructured tetrahedral meshes are illustrated by means of simple examples. These examples illustrate that the use of geometrical mesh quality measures alone may give misleading information and that mesh quality for problems modelling complex flows depends on the numerical error, the norm used to measure the error and the relationship between these quantities and the shape of the elements.