Search results for "LBB condition"

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Localized forms of the LBB condition and a posteriori estimates for incompressible media problems

2018

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 incompres…

General Computer ScienceMathematics::Analysis of PDEs01 natural sciencesMeasure (mathematics)Domain (mathematical analysis)Theoretical Computer SciencePhysics::Fluid DynamicsIncompressible flowBoundary value problem0101 mathematicsDivergence (statistics)Mathematicsta113LBB conditiona posteriori error estimatesNumerical AnalysisApplied Mathematics010102 general mathematicsMathematical analysista111010101 applied mathematicsincompressible viscous fluidsModeling and SimulationCompressibilityA priori and a posterioriConstant (mathematics)Mathematics and Computers in Simulation
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Localized forms of the LBB condition and a posteriori estimates for incompressible media problems

2018

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 …

Physics::Fluid DynamicsLBB conditiona posteriori error estimatesincompressible viscous fluidsMathematics::Analysis of PDEs
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