This is a summary of five lectures delivered at the CIME course on "Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" held in Cetraro, Italy, on June 1997.
Following the introductory lecture I -- which provides a general overview of approximate solution to nonlinear conservation laws, the remaining lectures deal with the specifics of four complementing topics:
Acknowledgment.I thank Alfio 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 #N00014-91-J-1076 and NSF grant #97-06827.
AMS Subject Classification. Primary 35L65, 35L60. Secondary 65M06, 65M12, 65M15, 65M60, 65M70