Geodesic
Construction of a natural norm for the convection-diffusion-reaction operator
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 335-355

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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. 
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     author = {Sangalli, Giancarlo},
     title = {Construction of a natural norm for the convection-diffusion-reaction operator},
     journal = {Bollettino della Unione matematica italiana},
     pages = {335--355},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {2},
     year = {2004},
     zbl = {1150.35455},
     mrnumber = {MR2072940},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a4/}
}
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Sangalli, Giancarlo. Construction of a natural norm for the convection-diffusion-reaction operator. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 335-355. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a4/