In this work, we construct, by means of the function space interpolation theory, a natural norm for a generic linear coercive and non-symmetric operator. We look for a norm which is the counterpart of the energy norm for symmetric operators. The natural norm allows for continuity and inf-sup conditions independent of the operator. Particularly we consider the convection-diffusion-reaction operator, for which we obtain continuity and inf-sup conditions that are uniform with respect to the operator coefficients, and therefore meaningful in the convectiondominant regime. Our results are preliminary to a deeper understanding and analysis of the numerical techniques for non-symmetric problems.
In questo lavoro si costruisce, mediante interpolazione, una norma naturale per operatori lineari continui coercivi e non simmetrici. Più precisamente, si cerca una norma con stesse le proprietà che ha la norma dell'energia quando si considerano operatori simmetrici: si dimostrano cioè, rispetto a tale norma, stime di continuità e di inf-sup indipendenti dall'operatore. In particolare, si prende in considerazione l'operatore di diffusione-trasporto-reazione lineare: si ottengono quindi stime di continuità e inf-sup indipendenti dai coefficienti dell'operatore, pertanto significative anche nel regime di trasporto dominante. I risultati qui presentati possono servire ad una più approfindita comprensione e analisi di tecniche numeriche per problemi non simmetrici.
@article{BUMI_2004_8_7B_2_335_0,
author = {Giancarlo Sangalli},
title = {Construction of a natural norm for the convection-diffusion-reaction operator},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {7-A},
year = {2004},
pages = {335-355},
zbl = {1150.35455},
mrnumber = {2072940},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_335_0}
}
Sangalli, Giancarlo. Construction of a natural norm for the convection-diffusion-reaction operator. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 335-355. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_335_0/
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