Search results for "Incompressible viscous fluid"

showing 3 items of 3 documents

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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Long time behavior for a dissipative shallow water model

2013

We consider the two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.

Inertial frame of referenceFourier splitting methodDynamical Systems (math.DS)Space (mathematics)Dynamical system01 natural sciencesPhysics::Fluid DynamicsNavier–Stokes equationsMathematics - Analysis of PDEsAttractorFOS: MathematicsMathematics - Dynamical Systems0101 mathematicsNavier–Stokes equationsPhysics::Atmospheric and Oceanic PhysicsMathematical PhysicsMathematicsApplied Mathematics010102 general mathematicsMathematical analysisAttractorIncompressible viscous fluidInertial manifoldFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsWaves and shallow waterTime decayDissipative systemCompressibilityAnalysisAnalysis of PDEs (math.AP)Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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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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