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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.
List of contents
General Introduction
R. Abgrall and C.-W. Shu
Introduction to the Theory of Hyperbolic Conservation Laws
C.M. Dafermos
The Riemann Problem: Solvers and Numerical Fluxes
E.F. Toro
Classical Finite Volume Methods
T. Sonar
Sharpening Methods for Finite Volume Schemes
B. Després, S. Kokh and F. Lagoutière
ENO and WENO Schemes
Y.-T. Zhang and C.-W. Shu
Stability Properties of the ENO Method
U.S. Fjordholm
Stability, Error Estimate and Limiters of Discontinuous Galerkin Methods
J. Qiu and Q. Zhang
HDG Methods for Hyperbolic Problems
B. Cockburn, N.C. Nguyen and J. Peraire
Spectral Volume and Spectral Difference Methods
Z.J. Wang, Y. Liu, C. Lacor and J. Azevedo
High-Order Flux Reconstruction Schemes
F.D. Witherden, P.E. Vincent and A. Jameson
Linear Stabilization for First-Order PDEs
A. Ern and J.-L. Guermond
Least-Squares Methods for Hyperbolic Problems
P. Bochev and M. Gunzburger
Staggered and Co-Located Finite Volume Schemes for Lagrangian
Hydrodynamics
R. Loubère, P.-H. Maire and B. Rebourcet
High Order Mass Conservative Semi-Lagrangian Methods for Transport Problems
J.-M. Qiu
Front Tracking Methods
D. She, R. Kaufman, H. Lim, J. Melvin, A. Hsu and J. Glimm
Moretti's Shock-Fitting Methods on Structured and Unstructured Meshes
A. Bonfiglioli, R. Paciorri, F. Nasuti and M. Onofri
Spectral Methods for Hyperbolic Problems
J.S. Hesthaven
Entropy Stable Schemes
E. Tadmor
Entropy Stable Summation-By-Parts Formulations for Compressible Computational Fluid Dynamics
M.H. Carpenter, T.C. Fisher, E.J. Nielsen, M. Parsani, M. Svärd and N. Yamaleev
Central Schemes: A Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs
A. Kurganov
Time Discretization Techniques
S. Gottlieb and D.I. Ketcheson
The Fast Sweeping Method for Stationary Hamilton-Jacobi Equations
H. Zhao
Numerical Methods for Hamilton?Jacobi Type Equations
M. Falcone and R. Ferretti
About the author
Rémi Abgrall is a professor at Universität ZürichProfessor Chi-Wang Shu is a professor at Brown University, RI, USA
