Numerical methods for conservation laws
By: Randall J. LeVeque.
Edition: 2nd ed.
Series: Lectures in mathematics ETH Zürich
Publisher: Birkhäuser Verlag
Published: 1992
Place of publication: Basel; Boston
Language: eng
Number of pages: 214
Subjects: Differential equations, Hyperbolic -- Numerical solutions; Conservation laws (Mathematics); Shock waves
Description: These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. The emphasis is on tools and techniques that are indispensable in developing good numerical methods for discontinuous solutions. Part II is devoted to the development of high resolution shock-capturing methods, including the theory of total variation diminishing (TVD) methods and the use of limiter functions. The book is intended for a wide audience, and will be of use both to numerical analysts and to computational researchers in a variety of applications.
Notes: Includes bibliographical references (p. 208-214).