Coverart for item
The Resource Computing Qualitatively Correct Approximations of Balance Laws : Exponential-Fit, Well-Balanced and Asymptotic-Preserving

Computing Qualitatively Correct Approximations of Balance Laws : Exponential-Fit, Well-Balanced and Asymptotic-Preserving

Label
Computing Qualitatively Correct Approximations of Balance Laws : Exponential-Fit, Well-Balanced and Asymptotic-Preserving
Title
Computing Qualitatively Correct Approximations of Balance Laws
Title remainder
Exponential-Fit, Well-Balanced and Asymptotic-Preserving
Creator
Subject
Language
eng
Summary
Substantial effort has been drawn for years onto the development of (possibly high-order) 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 space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curve
Member of
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 : Exponential-Fit, Well-Balanced and Asymptotic-Preserving
Instantiates
Publication
Note
3.2.1 Wave-Front 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 Crank-Nicolson to Scharfetter-Gummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1 The Leap from Crank-Nicolson to Scharfetter-Gummel 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 Well-Balanced to Control Stiffness and Averaging Errors1.2.1 Well-Balanced to Control Stiffness and Averaging Errors; 1x.(; 1x.(; 1.2.2 Singular Perturbation Theory and Asymptotic-Preserving; 1.2.2 Singular Perturbation Theory and Asymptotic-Preserving; 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 Non-Resonant 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 Initial-Boundary Value Problem and Large-Time Behavior; 2.1.3 Initial-Boundary Value Problem and Large-Time 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 Time-Exponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3 Time-Exponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3.2 Error Estimates for One-Dimensional Balance Laws
  • 2.3.2 Error Estimates for One-Dimensional Balance Laws2.3.3 Application to the Scalar Well-Balanced Scheme; 2.3.3 Application to the Scalar Well-Balanced 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 Non-ResonantWave-Front Tracking; 3.2 Error Estimate for Non-ResonantWave-Front 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
10.1007/978-88-470-2892-0
Specific material designation
remote
System control number
(OCoLC)857909916
Label
Computing Qualitatively Correct Approximations of Balance Laws : Exponential-Fit, Well-Balanced and Asymptotic-Preserving
Publication
Note
3.2.1 Wave-Front 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 Crank-Nicolson to Scharfetter-Gummel 1.1.1 Limitations for Gradients Computed with Finite Differences; 1.1 The Leap from Crank-Nicolson to Scharfetter-Gummel 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 Well-Balanced to Control Stiffness and Averaging Errors1.2.1 Well-Balanced to Control Stiffness and Averaging Errors; 1x.(; 1x.(; 1.2.2 Singular Perturbation Theory and Asymptotic-Preserving; 1.2.2 Singular Perturbation Theory and Asymptotic-Preserving; 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 Non-Resonant 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 Initial-Boundary Value Problem and Large-Time Behavior; 2.1.3 Initial-Boundary Value Problem and Large-Time 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 Time-Exponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3 Time-Exponential Error Estimate for the Godunov Scheme 2.3.1 Decay of Riemann Invariants and Temple Compactness; 2.3.2 Error Estimates for One-Dimensional Balance Laws
  • 2.3.2 Error Estimates for One-Dimensional Balance Laws2.3.3 Application to the Scalar Well-Balanced Scheme; 2.3.3 Application to the Scalar Well-Balanced 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 Non-ResonantWave-Front Tracking; 3.2 Error Estimate for Non-ResonantWave-Front 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
10.1007/978-88-470-2892-0
Specific material designation
remote
System control number
(OCoLC)857909916

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      38.944491 -92.326012
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