Continuous metrics and mesh optimization

Francois Courty David Leservoisier Paul-Louis George Alain Dervieux

Article in Applied Numerical Mathematics (29 pages)

Abstract: This paper addresses the problem of finding the mesh representing at best in L^p a twice continuous differentiable function defined on the plane. A continuous setting of this problem is used. It relies on an abstract mesh model, the “continuous metrics” allowing a variational analysis and on the identification of an optimum. Anisotropic optimal meshes can then be specified. An extension to discontinuities is proposed. It involves the prediction of the convergence order of the underlying mesh adaptation method. We present a few numerical illustrations related to numerical solution representation and to image compression.

Keywords: Mesh, Adaptation, Approximation, Interpolation, Compression, Metrics

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@article{CLGD06,
  author = {Courty, F. and Leservoisier, D. and George, P.-L. and Dervieux, A.},
  title = {Continuous metrics and mesh optimization},
  journal = {Applied Numerical Mathematics},
  volume = 56,
  pages = "117-145", 
  year = 2006
}