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.
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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     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/

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