Abstract
The Ladyzhenskaya-Babushka-Brezzi inequality (inf-sup-condition) is often used in the analysis of convergence of approximate solutions of hydrodynamic equations to exact ones. The constant involved in it depends on the shape of the domain and determines the efficiency of different algorithms. In this paper, its asymptotics and two-sided estimates for rectangular domains are obtained. To this end, a new method for estimating eigenvalues of a certain spectral problem with Stokes’ saddle operator is used.
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Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 387–396, March, 2000.
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Ol’shanskii, M.A., Chizhonkov, E.V. On the best constant in the inf-sup-condition for elongated rectangular domains. Math Notes 67, 325–332 (2000). https://doi.org/10.1007/BF02676669
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DOI: https://doi.org/10.1007/BF02676669