Geodesic
On a variant of the local projection method stable in the SUPG norm
Kybernetika, Tome 45 (2009) no. 4, pp. 634-645

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We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal $L^2$ projection with respect to a weighted $L^2$ inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
Classification : 65N12, 65N15, 65N30
Keywords: finite element method; convection-diffusion equation; stability; inf-sup condition; stabilization; SUPG method; local projection method; error estimates 
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     author = {Knobloch, Petr},
     title = {On a variant of the local projection method stable in the {SUPG} norm},
     journal = {Kybernetika},
     pages = {634--645},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2009},
     mrnumber = {2588629},
     zbl = {1191.65155},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a7/}
}
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Knobloch, Petr. On a variant of the local projection method stable in the SUPG norm. Kybernetika, Tome 45 (2009) no. 4, pp. 634-645. http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a7/