Advanced Numerical Approximation of Nonlinear Hyperbolic Equations 3 C. Johnson: Adaptive Finite Element Methods for Conservation Laws Approximate Solutions of Nonlinear Conservation Laws

This is a summary of ve lectures delivered at the CIME course on Advanced Nu merical Approximation of Nonlinear Hyperbolic Equations held in Cetraro Italy on June Following the introductory lecture I which provides a general overview of approximate solution to nonlinear conservation laws the remaining lectures deal with the speci cs of four complementing topics Lecture II Finite di erence methods non oscillatory central schemes Lecture III Spectral approximations the Spectral Viscosity method Lecture IV Convergence rate estimates a Lip convergence theory Lecture V Kinetic approximations regularity of kinetic formulations Acknowledgements I thank Al o Quarteroni for the invitation B Cockburn C Johnson C W Shu for the team discussions the Italian participants for their attention and the hosting Grand Hotel at San Michele for its remarkably unique atmosphere Research was supported in part by ONR grant N J and NSF grant AMS Subject Classi cation Primary L L Secondary M M M M M