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BL
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| Record Number
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864053
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| Title & Author
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Uncertainty quantification for hyperbolic and kinetic equations /\ Shi Jin, Lorenzo Pareschi, editors.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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| Series Statement
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SEMA SIMAI Springer series,; volume 14
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| Page. NO
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1 online resource :: illustrations (some color)
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| ISBN
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3319671103
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: 9783319671109
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331967109X
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9783319671093
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; Contents; About the Editors; The Stochastic Finite Volume Method; 1 Introduction; 1.1 Deterministic Scalar Hyperbolic Conservation Laws; 1.2 Stochastic Conservation Laws; 1.3 Random Fields and Probability Spaces; 2 General Framework; 2.1 General Principles; 2.2 A First Example: The Kraichnan-Orszag Three-Mode Problem; 2.2.1 One Random Variable; 2.2.2 Two Random Variables; 3 Stochastic Finite Volume Method on Cartesian Grids; 3.1 Stochastic Finite Volume Method; 3.2 Numerical Convergence Analysis; 3.3 Numerical Results; 3.3.1 Buckley-Leverett Equation
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3.1 Decomposition of the Transport Solution4 Uncertainty Propagation in Transport Equations; 4.1 Uncertainty Modeling for the Constitutive Coefficients; 4.1.1 Stationarity, Ergodicity, and Mixing Properties; 4.2 Homogenization Result and the Convergence Rate; 4.3 Central Limit Theory for the Random Fluctuations; 4.4 Further Remarks; 4.4.1 Long Range Correlated Random Media; 4.4.2 Moments Estimates for Mixing Random Fields; References; Numerical Methods for High-Dimensional Kinetic Equations; 1 Introduction; 2 Numerical Methods; 2.1 Sparse Grids; 2.2 Low-Rank Tensor Approximation
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3.10 Anisotropic Mesh Adaptation for Euler Equations3.11 Numerical Approximation of the Probability Density Function; 4 Stochastic Finite Volume Method on Unstructured Grids; 4.1 Mixed DG/FV Formulation; 4.2 Numerical Results; 4.2.1 Stochastic Cloud-Shock Interaction Problem (Random Flux); 4.2.2 Forward-Facing Step Channel; 4.2.3 Stochastic Cloud-Shock Interaction Problem (Random IC); 4.2.4 Flow Past a Cylinder; 4.2.5 Flow Around NACA0012 Airfoil; 4.2.6 Flow Around NACA23012 Airfoil with Flap; 4.2.7 Flow Around RAE2822 Airfoil; 4.3 Parallel Algorithm and Parallel Efficiency of the SFVM
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3.3.2 Stochastic Sod's Shock Tube Problem with Random Initial Data3.3.3 Stochastic Sod's Shock Tube Problem with Random Flux and Initial Data; 3.4 Adaptive Parametrization of the Stochastic Space for SFVM; 3.5 Efficiency of the SFVM; 3.6 SFVM Error Estimates for the Statistical Solution; 3.7 Estimates in L∞-Norm; 3.7.1 Error Estimate for the Mean Eh[uh]; 3.7.2 Error Estimate for the Variance Vh[uh]; 3.8 Estimates in L1-Norm; 3.8.1 Convergence of Eh[uhxy] in L1-Norm; 3.8.2 Convergence of Vh[uhxy] in L1-Norm; 3.9 Error vs Work Estimates for SFVM
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5 Other Applications5.1 Nozzle Flow with Shock; 5.2 Application with Other Schemes; 5.3 Overcoming the Curse of Dimensionality; 5.4 Applications for Multiphase Flows; 6 Conclusions; References; Uncertainty Modeling and Propagation in Linear Kinetic Equations; 1 Introduction; 2 Uncertainties in the Derivation of Kinetic Equations; 2.1 Setting of the Problem; 2.2 The Paraxial Regime; 2.3 High Frequency Limit; 2.3.1 The Wave Equation; 2.3.2 The Schrödinger Equation; 2.4 Corrector Analysis; 2.4.1 The Itô-Schrödinger Regime; 2.4.2 Other Regimes; 3 Transport Equation
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| Subject
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Differential equations, Hyperbolic.
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| Subject
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Uncertainty (Information theory)
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Differential equations, Hyperbolic.
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| Subject
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MATHEMATICS-- Calculus.
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| Subject
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MATHEMATICS-- Mathematical Analysis.
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| Subject
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Uncertainty (Information theory)
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| Dewey Classification
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515/.353
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| LC Classification
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QA374
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| Added Entry
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Jin, Shi,1963-
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Pareschi, Lorenzo
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