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Isotropic and Anisotropic Adaptive Meshes : Models and Convergence Properties

  • A. Dervieux
  • D. Leservoisier
  • B. Palmerio
  • Y. Coudière
Conference paper
  • 262 Downloads
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 78)

Summary

We review shortly two mathematical notions for mesh adaption, the order of convergence when the number of nodes is considered, and the functional model of continuous metrics. We point out the rather poor convergence properties of isotropic mesh adaption strategies, by exhibiting a barrier for the order of convergence. We show that the continuous metrics concept opens the door too an elegant derivation of optimal mesh adaption. These ideas are presented in the simplified case of mesh adaptive interpolation or compression. We dedicate this work to Professor Satofuka, expressing our admiration for the work of the scientist and our friendliness for our colleague.

Keywords

Mesh Adaption Adaptive Mesh Refinement Mesh Adaptation Continuous Metrics Finite Element Interpolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    H. Boronchaki, P. L. George and B. Moharnmadi, “ Delaunay mesh generation governed by metric specifications. Part 2: Application examples”. Finite Elements in Analysis and Design 25, 1997, p. 85–109.MathSciNetCrossRefGoogle Scholar
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    D. Leservoisier, Paul-Louis George, A. Dervieux, “ Métrique continue et optimisation de maillage”, INRIA Research Report, 2000Google Scholar
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    D. Leservoisier, P.-L. George, O. Penanhoat, A. Dervieux, “ Application of mesh-adaptive techniques to mesh convergence in complex CFD Second international symposium on Finite Volumes”, for Complex Applications, Problems and Perspectives, université de Duisbourg, july 1999, Finite Volumes for Complex Applications, R. Vilsmeier, F. Benkhaldoun, D. Haenel, Eds., Hernies Science Pub., 1999, 817–824Google Scholar
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    D. Leservoisier, Paul-Louis George, A. Dervieux, O. Penanhoat, “ Mesh Adaption as a tool for certified numerics”, ICCFD, Kyoto, june 2000Google Scholar
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    B. Palmerio, Y. Coudière, D. Leservoisier, A. Dervieux, “ Barriers in mesh adaptive convergencs for isotropic strategies”, INRIA Research Report, decemnber 2000Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • A. Dervieux
    • 1
  • D. Leservoisier
    • 2
    • 3
  • B. Palmerio
    • 4
  • Y. Coudière
    • 1
  1. 1.INRIASophia-AntipolisFrance
  2. 2.SNECMA VillarocheMoissy CramayelFrance
  3. 3.INRIAFrance
  4. 4.Laboratoire de MathématiquesUniversité de Nice et Sophia-AntipolisNiceFrance

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