Mesh Quality: A Function of Geometry, Error Estimates or Both

Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.229-238, October 1998

MESHING
RESEARCH
CORNER

7th International Meshing Roundtable
October 26-28, 1998
Dearborn, Michigan, USA

Abstract
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. A survey of more recent work in the development of finite element methods reveals work on anisotropic meshing algorithms and on providing good error estimates that reveal the relationship between the error and both the mesh and the solution gradients. The realities of solving complex three dimensional problems is that such indicators are presently not available for many problems of interest. A simple tetrahedral mesh quality measure using both geometrical and solution information will be described. Some of the issues in mesh quality for unstructured tetrahedral meshes will be illustrated by means of a simple example.

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