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

Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications Written by leading subject experts in each field who provide breadth and depth of content coverage