In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems are analyzed. Finally, numerical test cases are provided to assess the soundness of the proposed approach.
In questa comunicazione vengono presentate tecniche di adattazione di griglia goal-oriented di tipo anisotropo. Punto di partenza è stata la derivazione di opportune stime di tipo anisotropo per l'errore d'interpolazione, per elementi finiti lineari a pezzi, su griglie triangolari in . Si sono quindi utilizzate tali stime d'interpolazione per generalizzare al caso anisotropo l'analisi a posteriori proposta da R. Rannacher e da R. Becker, basata su un approccio di tipo duale. In questo lavoro tale analisi a posteriori viene particolarizzata al caso di problemi ellittici, di trasporto-diffusione-reazione e al problema di Stokes. Vengono da ultimo forniti alcuni risultati numerici al fine di validare laffidabilità dellapproccio proposto
@article{BUMI_2005_8_8B_1_145_0,
author = {Simona Perotto},
title = {Anisotropic mesh adaption: application to computational fluid dynamics},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {145-165},
zbl = {1150.65028},
mrnumber = {2122980},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_1_145_0}
}
Perotto, Simona. Anisotropic mesh adaption: application to computational fluid dynamics. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 145-165. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_1_145_0/
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