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Handbook of Numerical Methods for Hyperbolic Problems Basic and Fundamental Issues

✍ Scribed by Rémi Abgrall and Chi-Wang Shu (Eds.)

Publisher
North Holland
Year
2016
Tongue
English
Leaves
640
Series
Handbook of Numerical Analysis Volume 17
Edition
1st Edition
Category
Library
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✦ Synopsis

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations.

This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.

✦ Table of Contents

Content:
Series PagePage ii
CopyrightPage iv
ContributorsPages xvii-xix
IntroductionPages xxi-xxiiiR. Abgrall, C.-W. Shu
Chapter 1 - Introduction to the Theory of Hyperbolic Conservation LawsPages 1-18C.M. Dafermos
Chapter 2 - The Riemann Problem: Solvers and Numerical FluxesPages 19-54E.F. Toro
Chapter 3 - Classical Finite Volume MethodsPages 55-76T. Sonar
Chapter 4 - Sharpening Methods for Finite Volume SchemesPages 77-102B. Després, S. Kokh, F. Lagoutière
Chapter 5 - ENO and WENO SchemesPages 103-122Y.-T. Zhang, C.-W. Shu
Chapter 6 - Stability Properties of the ENO MethodPages 123-145U.S. Fjordholm
Chapter 7 - Stability, Error Estimate and Limiters of Discontinuous Galerkin MethodsPages 147-171J. Qiu, Q. Zhang
Chapter 8 - HDG Methods for Hyperbolic ProblemsPages 173-197B. Cockburn, N.C. Nguyen, J. Peraire
Chapter 9 - Spectral Volume and Spectral Difference MethodsPages 199-226Z.J. Wang, Y. Liu, C. Lacor, J.L.F. Azevedo
Chapter 10 - High-Order Flux Reconstruction SchemesPages 227-263F.D. Witherden, P.E. Vincent, A. Jameson
Chapter 11 - Linear Stabilization for First-Order PDEsPages 265-288A. Ern, J.-L. Guermond
Chapter 12 - Least-Squares Methods for Hyperbolic ProblemsPages 289-317P. Bochev, M. Gunzburger
Chapter 13 - Staggered and Colocated Finite Volume Schemes for Lagrangian HydrodynamicsPages 319-352R. Loubère, P.-H. Maire, B. Rebourcet
Chapter 14 - High-Order Mass-Conservative Semi-Lagrangian Methods for Transport ProblemsPages 353-382J.-M. Qiu
Chapter 15 - Front-Tracking MethodsPages 383-402D. She, R. Kaufman, H. Lim, J. Melvin, A. Hsu, J. Glimm
Chapter 16 - Moretti's Shock-Fitting Methods on Structured and Unstructured MeshesPages 403-439A. Bonfiglioli, R. Paciorri, F. Nasuti, M. Onofri
Chapter 17 - Spectral Methods for Hyperbolic Problems1Pages 441-466J.S. Hesthaven
Chapter 18 - Entropy Stable SchemesPages 467-493E. Tadmor
Chapter 19 - Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid DynamicsPages 495-524M.H. Carpenter, T.C. Fisher, E.J. Nielsen, M. Parsani, M. Svärd, N. Yamaleev
Chapter 20 - Central Schemes: A Powerful Black-Box Solver for Nonlinear Hyperbolic PDEsPages 525-548A. Kurganov
Chapter 21 - Time Discretization TechniquesPages 549-583S. Gottlieb, D.I. Ketcheson
Chapter 22 - The Fast Sweeping Method for Stationary Hamilton–Jacobi EquationsPages 585-601H. Zhao
Chapter 23 - Numerical Methods for Hamilton–Jacobi Type EquationsPages 603-626M. Falcone, R. Ferretti
IndexPages 627-641

✦ Subjects

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