Engineering with Computers

, Volume 15, Issue 3, pp 236–247 | Cite as

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

  • M. Berzins
Original Article


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 research in the development of finite element methods describes 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 reality 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 is described. Some of the issues in mesh quality for unstructured tetrahedral meshes are illustrated by means of two simple examples.

Key words. Error estimates; Mesh generation; Mesh quality; Unstructured meshes 


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Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • M. Berzins
    • 1
  1. 1.Computational PDEs Unit, School of Computer Studies, The University, Leeds, UKGB

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