Planar mesh refinement cannot be both local and regular |
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Authors: | JF Buss RB Simpson |
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Institution: | (1) Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 , CA |
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Abstract: | We show that two desirable properties for planar mesh refinement techniques are incompatible. Mesh refinement is a common
technique for adaptive error control in generating unstructured planar triangular meshes for piecewise polynomial representations
of data. Local refinements are modifications of the mesh that involve a fixed maximum amount of computation, independent of
the number of triangles in the mesh. Regular meshes are meshes for which every interior vertex has degree 6. At least for
some simple model meshing problems, optimal meshes are known to be regular, hence it would be desirable to have a refinement
technique that, if applied to a regular mesh, produced a larger regular mesh. We call such a technique a regular refinement.
In this paper, we prove that no refinement technique can be both local and regular. Our results also have implications for
non-local refinement techniques such as Delaunay insertion or Rivara's refinement.
Received August 1, 1996 / Revised version received February 28, 1997 |
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Keywords: | Mathematics Subject Classification (1991):65N50 |
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