The Resource Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving
Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving
Resource Information
The item Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 Substantial effort has been drawn for years onto the development of (possibly highorder) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or spacedependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curve
 Language
 eng
 Extent
 1 online resource (346 pages).
 Note
 3.2.1 WaveFront Tracking Approximations
 Contents

 TitlePage; Copyright; Preface; Acknowledgements; Acronyms; Contents; Introduction and Chronological Perspective; 1.1 The Leap from CrankNicolson to ScharfetterGummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1 The Leap from CrankNicolson to ScharfetterGummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1.2 Numerical Gradients as Local First Integrals of the Motion; 1.1.2 Numerical Gradients as Local First Integrals of the Motion; 1v>; 1v>; 1v<; 1v<; 1.2 Modular Programming and Its Shortcomings; 1.2 Modular Programming and Its Shortcomings
 1.2.1 WellBalanced to Control Stiffness and Averaging Errors1.2.1 WellBalanced to Control Stiffness and Averaging Errors; 1x.(; 1x.(; 1.2.2 Singular Perturbation Theory and AsymptoticPreserving; 1.2.2 Singular Perturbation Theory and AsymptoticPreserving; 1.3 Organization of the Book; 1.3 Organization of the Book; 1.3.1 Hyperbolic Systems of Balance Laws; 1.3.1 Hyperbolic Systems of Balance Laws; 1.3.2 Weakly Nonlinear Kinetic Equations; 1.3.2 Weakly Nonlinear Kinetic Equations; References; References; Part I; Lifting a NonResonant Scalar Balance Law
 2.1 Generalities about Scalar Laws with Source Terms2.1 Generalities about Scalar Laws with Source Terms; 2.1.1 Method of Characteristics and Shocks; 2.1.1 Method of Characteristics and Shocks; 2.1.2 Entropy Solution and Kružkov Theory; 2.1.2 Entropy Solution and Kružkov Theory; 2.1.3 InitialBoundary Value Problem and LargeTime Behavior; 2.1.3 InitialBoundary Value Problem and LargeTime Behavior; 2.2 Localization Process of the Source Term on a Discrete Lattice; 2.2 Localization Process of the Source Term on a Discrete Lattice; 2.2.1 Nonconservative Lifting of an Inhomogeneous Equation
 2.2.1 Nonconservative Lifting of an Inhomogeneous Equation1; 1; 2.2.2 The Measure Source Term Revealed by the Weaklimit; 2.2.2 The Measure Source Term Revealed by the Weaklimit; 2.2.3 A L1 Contraction Result "à la Kružkov"; 2.2.3 A L1 Contraction Result "à la Kružkov"; 2.3 TimeExponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3 TimeExponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3.2 Error Estimates for OneDimensional Balance Laws
 2.3.2 Error Estimates for OneDimensional Balance Laws2.3.3 Application to the Scalar WellBalanced Scheme; 2.3.3 Application to the Scalar WellBalanced Scheme; Notes; Notes; References; References; Lyapunov Functional for Linear Error Estimates; 3.1 Preliminaries 3.1.1 A Puzzling Numerical Example; 3.1 Preliminaries 3.1.1 A Puzzling Numerical Example; 3.1.2 Lifting of the Balance Law: Temple System Reformulation; 3.1.2 Lifting of the Balance Law: Temple System Reformulation; 3.2 Error Estimate for NonResonantWaveFront Tracking; 3.2 Error Estimate for NonResonantWaveFront Tracking
 Isbn
 9788847028920
 Label
 Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving
 Title
 Computing Qualitatively Correct Approximations of Balance Laws
 Title remainder
 ExponentialFit, WellBalanced and AsymptoticPreserving
 Language
 eng
 Summary
 Substantial effort has been drawn for years onto the development of (possibly highorder) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or spacedependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curve
 Cataloging source
 MEAUC
 http://library.link/vocab/creatorName
 Gosse, Laurent
 Dewey number
 620.11232
 Index
 index present
 LC call number
 QA931 .G384 2013
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SIMAI Springer Series
 Series volume
 v. 2
 http://library.link/vocab/subjectName

 Elasticity
 Conservation laws (Mathematics)
 SCIENCE
 Conservation laws (Mathematics)
 Elasticity
 Label
 Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving
 Note
 3.2.1 WaveFront Tracking Approximations
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 TitlePage; Copyright; Preface; Acknowledgements; Acronyms; Contents; Introduction and Chronological Perspective; 1.1 The Leap from CrankNicolson to ScharfetterGummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1 The Leap from CrankNicolson to ScharfetterGummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1.2 Numerical Gradients as Local First Integrals of the Motion; 1.1.2 Numerical Gradients as Local First Integrals of the Motion; 1v>; 1v>; 1v<; 1v<; 1.2 Modular Programming and Its Shortcomings; 1.2 Modular Programming and Its Shortcomings
 1.2.1 WellBalanced to Control Stiffness and Averaging Errors1.2.1 WellBalanced to Control Stiffness and Averaging Errors; 1x.(; 1x.(; 1.2.2 Singular Perturbation Theory and AsymptoticPreserving; 1.2.2 Singular Perturbation Theory and AsymptoticPreserving; 1.3 Organization of the Book; 1.3 Organization of the Book; 1.3.1 Hyperbolic Systems of Balance Laws; 1.3.1 Hyperbolic Systems of Balance Laws; 1.3.2 Weakly Nonlinear Kinetic Equations; 1.3.2 Weakly Nonlinear Kinetic Equations; References; References; Part I; Lifting a NonResonant Scalar Balance Law
 2.1 Generalities about Scalar Laws with Source Terms2.1 Generalities about Scalar Laws with Source Terms; 2.1.1 Method of Characteristics and Shocks; 2.1.1 Method of Characteristics and Shocks; 2.1.2 Entropy Solution and Kružkov Theory; 2.1.2 Entropy Solution and Kružkov Theory; 2.1.3 InitialBoundary Value Problem and LargeTime Behavior; 2.1.3 InitialBoundary Value Problem and LargeTime Behavior; 2.2 Localization Process of the Source Term on a Discrete Lattice; 2.2 Localization Process of the Source Term on a Discrete Lattice; 2.2.1 Nonconservative Lifting of an Inhomogeneous Equation
 2.2.1 Nonconservative Lifting of an Inhomogeneous Equation1; 1; 2.2.2 The Measure Source Term Revealed by the Weaklimit; 2.2.2 The Measure Source Term Revealed by the Weaklimit; 2.2.3 A L1 Contraction Result "à la Kružkov"; 2.2.3 A L1 Contraction Result "à la Kružkov"; 2.3 TimeExponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3 TimeExponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3.2 Error Estimates for OneDimensional Balance Laws
 2.3.2 Error Estimates for OneDimensional Balance Laws2.3.3 Application to the Scalar WellBalanced Scheme; 2.3.3 Application to the Scalar WellBalanced Scheme; Notes; Notes; References; References; Lyapunov Functional for Linear Error Estimates; 3.1 Preliminaries 3.1.1 A Puzzling Numerical Example; 3.1 Preliminaries 3.1.1 A Puzzling Numerical Example; 3.1.2 Lifting of the Balance Law: Temple System Reformulation; 3.1.2 Lifting of the Balance Law: Temple System Reformulation; 3.2 Error Estimate for NonResonantWaveFront Tracking; 3.2 Error Estimate for NonResonantWaveFront Tracking
 Control code
 857909916
 Dimensions
 unknown
 Extent
 1 online resource (346 pages).
 Form of item
 online
 Isbn
 9788847028920
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9788847028920
 Specific material designation
 remote
 System control number
 (OCoLC)857909916
 Label
 Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving
 Note
 3.2.1 WaveFront Tracking Approximations
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 TitlePage; Copyright; Preface; Acknowledgements; Acronyms; Contents; Introduction and Chronological Perspective; 1.1 The Leap from CrankNicolson to ScharfetterGummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1 The Leap from CrankNicolson to ScharfetterGummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1.2 Numerical Gradients as Local First Integrals of the Motion; 1.1.2 Numerical Gradients as Local First Integrals of the Motion; 1v>; 1v>; 1v<; 1v<; 1.2 Modular Programming and Its Shortcomings; 1.2 Modular Programming and Its Shortcomings
 1.2.1 WellBalanced to Control Stiffness and Averaging Errors1.2.1 WellBalanced to Control Stiffness and Averaging Errors; 1x.(; 1x.(; 1.2.2 Singular Perturbation Theory and AsymptoticPreserving; 1.2.2 Singular Perturbation Theory and AsymptoticPreserving; 1.3 Organization of the Book; 1.3 Organization of the Book; 1.3.1 Hyperbolic Systems of Balance Laws; 1.3.1 Hyperbolic Systems of Balance Laws; 1.3.2 Weakly Nonlinear Kinetic Equations; 1.3.2 Weakly Nonlinear Kinetic Equations; References; References; Part I; Lifting a NonResonant Scalar Balance Law
 2.1 Generalities about Scalar Laws with Source Terms2.1 Generalities about Scalar Laws with Source Terms; 2.1.1 Method of Characteristics and Shocks; 2.1.1 Method of Characteristics and Shocks; 2.1.2 Entropy Solution and Kružkov Theory; 2.1.2 Entropy Solution and Kružkov Theory; 2.1.3 InitialBoundary Value Problem and LargeTime Behavior; 2.1.3 InitialBoundary Value Problem and LargeTime Behavior; 2.2 Localization Process of the Source Term on a Discrete Lattice; 2.2 Localization Process of the Source Term on a Discrete Lattice; 2.2.1 Nonconservative Lifting of an Inhomogeneous Equation
 2.2.1 Nonconservative Lifting of an Inhomogeneous Equation1; 1; 2.2.2 The Measure Source Term Revealed by the Weaklimit; 2.2.2 The Measure Source Term Revealed by the Weaklimit; 2.2.3 A L1 Contraction Result "à la Kružkov"; 2.2.3 A L1 Contraction Result "à la Kružkov"; 2.3 TimeExponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3 TimeExponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3.2 Error Estimates for OneDimensional Balance Laws
 2.3.2 Error Estimates for OneDimensional Balance Laws2.3.3 Application to the Scalar WellBalanced Scheme; 2.3.3 Application to the Scalar WellBalanced Scheme; Notes; Notes; References; References; Lyapunov Functional for Linear Error Estimates; 3.1 Preliminaries 3.1.1 A Puzzling Numerical Example; 3.1 Preliminaries 3.1.1 A Puzzling Numerical Example; 3.1.2 Lifting of the Balance Law: Temple System Reformulation; 3.1.2 Lifting of the Balance Law: Temple System Reformulation; 3.2 Error Estimate for NonResonantWaveFront Tracking; 3.2 Error Estimate for NonResonantWaveFront Tracking
 Control code
 857909916
 Dimensions
 unknown
 Extent
 1 online resource (346 pages).
 Form of item
 online
 Isbn
 9788847028920
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9788847028920
 Specific material designation
 remote
 System control number
 (OCoLC)857909916
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/ComputingQualitativelyCorrectApproximationsof/3i474mktuZo/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/ComputingQualitativelyCorrectApproximationsof/3i474mktuZo/">Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/ComputingQualitativelyCorrectApproximationsof/3i474mktuZo/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/ComputingQualitativelyCorrectApproximationsof/3i474mktuZo/">Computing Qualitatively Correct Approximations of Balance Laws : ExponentialFit, WellBalanced and AsymptoticPreserving</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>