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Metric tensor recovery for adaptive meshing

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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https://hal.inria.fr/hal-01271671
Contributor : Patrick Laug <>
Submitted on : Tuesday, February 9, 2016 - 3:00:00 PM
Last modification on : Monday, May 4, 2020 - 9:06:07 AM

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Patrick Laug, Houman Borouchaki. Metric tensor recovery for adaptive meshing. Mathematics and Computers in Simulation, Elsevier, 2015, ⟨10.1016/j.matcom.2015.02.004⟩. ⟨hal-01271671⟩

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