*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:
*

- Lecture II. Finite-difference 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.

4in

*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.

1in

**AMS Subject Classification**.
Primary 35L65, 35L60. Secondary
65M06, 65M12, 65M15, 65M60, 65M70

- Contents
- Non-oscillatory central schemes
- References
- Kinetic Formulations and Regularity
- References
- About this document ...

Mon Dec 8 17:34:34 PST 1997