numerical methods for conservation laws lectures in mathematics eth z

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Numerical Methods For Conservation Laws

Author : LEVEQUE
ISBN : 9783034851169
Genre : Juvenile Nonfiction
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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.

Proceedings Of The Ninth Gamm Conference On Numerical Methods In Fluid Mechanics

Author : Jan B. Vos
ISBN : 9783663139744
Genre : Technology & Engineering
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Numerical Methods For Conservation Laws

Author : Randall J. LeVeque
ISBN : STANFORD:36105113906429
Genre : Conservation laws (Mathematics)
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Analytische Methoden In Der Theorie Der Erhaltungsgleichungen

Author :
ISBN : 9783663092643
Genre : Technology & Engineering
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Das Buch ist eine umfassende Darstellung der Beweismethodik des Existenzsatzes von Oleinik für skalare Erhaltungsgleichungen, den Tartar mit der Methode der kompensierten Kompaktheit gegeben hat. Dabei kommen verfeinerte Kompaktheitsargumente für schwach konvergente Folgen und eine Fülle analytischer Methoden zum Einsatz, die erheblich über die übliche Verwendung kompakter Einbettungen von Funktionenräumen hinausgehen. Der Text setzt nur die üblichen Grundkenntnisse der Analysis und der linearen Funktionalanalysis voraus. Kern des Buches sind vier Kapitel über schwache Konvergenz, verallgemeinerte Quasikonvexität, kompensierte Kompaktheit und Youngsche Maße. Im letzten Kapitel werden schwache Lösungen, maßwertige Lösungen, Entropiebedingungen und der Existenzbeweis von Tartar diskutiert. Das Buch eignet sich als Grundlage einer einsemestrigen Vorlesung oder eines Seminars.

Numerical Approximation Of Hyperbolic Systems Of Conservation Laws

Author : Edwige Godlewski
ISBN : 9781461207139
Genre : Mathematics
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This work is devoted to the theory and approximation of nonlinear hyper bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.

Hyperbolic Partial Differential Equations

Author : Peter D. Lax
ISBN : 9780821835760
Genre : Mathematics
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The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses.

Splinefunktionen

Author : Carl de Boor
ISBN : 9783034891332
Genre : Science
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Internationale Mathematische Nachrichten

Author :
ISBN : CORNELL:31924074884572
Genre : Mathematics
File Size : 77. 46 MB
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Bonner Mathematische Schriften

Author :
ISBN : UCSD:31822022898951
Genre : Mathematics
File Size : 29. 14 MB
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Viskosit Tsapproximationen Und Schwache L Sungen F R Das System Der Eindimensionalen Nichtlinearen Elastizit Tsgleichungen

Author : Dieter Göbel
ISBN : UOM:39015033251565
Genre : Approximation theory
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