 Localized forms of the LBB condition and a posteriori estimates for incompressible media problemsS. Repin Mathematics and Computers in Simulation (MATCOM), 2018, vol. 145, issue C, 156-170 Abstract: The inf–sup (or LBB) condition plays a crucial role in analysis of viscous flow problems and other problems related to incompressible media. In this paper, we deduce localized forms of this condition that contain a collection of local constants associated with subdomains instead of one global constant for the whole domain. Localized forms of the LBB inequality imply estimates of the distance to the set of divergence free fields. We use them and deduce fully computable bounds of the distance between approximate and exact solutions of boundary value problems arising in the theory of viscous incompressible fluids. The estimates are valid for approximations, which satisfy the incompressibility condition only in a very weak (integral) form. Another important question considered in the paper is how to select proper measures that should be used in error analysis. We show that such a measure is dictated by the respective error identity and discuss properties of the measure for the Stokes, Oseen, and Navier–Stokes problems. Keywords: Incompressible viscous fluids; LBB condition; A posteriori error estimates (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:145:y:2018:i:c:p:156-170 DOI: 10.1016/j.matcom.2016.05.004 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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