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Approximate solutions of nonlinear conservation laws

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Book cover Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1697))

Abstract

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.

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  1. Department of Mathematics, UCLA, 90095, Los-Angeles, CA

    Eitan Tadmor

  2. School of Mathematical Sciences, Tel-Aviv University, 69978, Tel-Aviv

    Eitan Tadmor

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Tadmor, E. (1998). Approximate solutions of nonlinear conservation laws. In: Quarteroni, A. (eds) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics, vol 1697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096352

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