The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant.
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
The numerical techniques developed in this paper are designed to solve two
problems : hyperbolic conservation problems with ... Also , we treat three different
types of singularity arising in inviscid and viscous conservation laws , using
Author: Institute for Computer Applications in Science and Engineering
This Software Requirements Specification (SRS) specifies the engineering and qualification requirements for the Slide Show CSCI of the Mapping and Graphic Information Capability (MAGIC). Furthermore, this specification will be used as the basis for the design and formal testing of that CSCI. The SRS is divided into three major sections. These sections cover Engineering Requirements (Section 3), Qualification Requirements (Section 4), and Preparation for Delivery (Section 5). This specification supersedes the Rational-generated Interface Requirements Specification (configuration identifier 8734/89-IRS-GIPSY-003) for the Modernized Graphic Information Presentation System (GIPSY) that was delivered under Contract Number DCA100-89- C-0015 and dated 13 September 1989.
Written by a well-known expert in the field, the focus of this book is on an innovative mathematical and numerical theory which applies to classical models of physics such as shock waves and balance laws.
Author: Benoit Perthame
Publisher: Oxford University Press
Written by a well-known expert in the field, the focus of this book is on an innovative mathematical and numerical theory which applies to classical models of physics such as shock waves and balance laws. The text is based on early works in common with P.L. Lions (field medalist).
Bernardo Cockburn, Institute for Computer Applications in Science and
Engineering. piecewise - linear and piecewise - quadratic approximations in both
triangular and rectangular elements . 3.1 Fluxes For the numerical flux needed in
( 2.4 ) ...
Author: Bernardo Cockburn
This is the fifth paper in a series in which we construct and study the so-called Range-Kutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters, both in the triangular and the rectangular element cases. Numerical experiments for two dimensional Euler equations of compressible gas dynamics are presented that show the effect of the (formal) order of accuracy and the use of triangles or rectangles, on the quality of the approximation.
A random choice finite difference scheme for hyperbolic conservation laws . '
SIAM Journal Numerical Analysis , 18 , 289-315 . Harten , A. , Lax , P. D. , and
Van Leer , B. ( 1983 ) . " On upstream differencing and Godunov - type schemes
Author: Ch Hirsch
Publisher: John Wiley & Sons
The second of two volumes which together provide a comprehensive account of the numerical computation of internal and external flows, this work deals with the application of computational methods to the problems of fluid dynamics.
This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws.
Author: Constantine M. Dafermos
This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: "This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews