# Metric tensor recovery for adaptive meshing

1 Gamma3 - Automatic mesh generation and advanced methods
Inria Paris-Rocquencourt, UTT - Université de Technologie de Troyes
Abstract : Adaptive computation is now recognized as essential for solving complex PDE problems. Conceptually, such a computation requires at each step the definition of a continuous metric field (mesh size and direction) to govern the generation of adapted meshes. In practice, in the adaptive computation, an appropriate {\it a posteriori\/} error estimation is used and an upper-bounding of the error is expressed in terms of discrete metrics associated with the element vertices. In order to obtain a continuous metric field, the discrete field is recovered in the whole domain mesh using an appropriate interpolation method on each element. In this paper, a new method for interpolating discrete metric fields, based on a so-called natural decomposition'' of metrics, is introduced. The proposed method uses known matrix decompositions and is computationally robust and efficient. Classical interpolation methods are recalled and, from numerical examples on simplicial mesh elements, some qualitative comparisons against the new methodology are made to show its relevance.
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Article dans une revue
International Journal of Mathematics and Computers in Simulation, 2015, 〈10.1016/j.matcom.2015.02.004〉

https://hal.inria.fr/hal-01271671
Contributeur : Patrick Laug <>
Soumis le : mardi 9 février 2016 - 15:00:00
Dernière modification le : mardi 17 avril 2018 - 11:29:34

### Citation

Patrick Laug, Houman Borouchaki. Metric tensor recovery for adaptive meshing. International Journal of Mathematics and Computers in Simulation, 2015, 〈10.1016/j.matcom.2015.02.004〉. 〈hal-01271671〉

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