Title: Advanced numerical approximation of nonlinear hyperbolic equations
Description: This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.
Subjects: Hyperbolic Differential equations, Numerical solutions, Nonlinear Differential equations, Congresses, Differential equations, hyperbolic, Differential equations, nonlinear, Mathematics, Differential equations, partial, Numerical analysis, Thermodynamics