Advanced Numerical Approximation Of Nonlinear Hyperbolic Equations

Author : B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
Publisher : Springer
Page : 446 pages
File Size : 49,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540498049

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations by B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor Pdf

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Author : Anonim
Publisher : Unknown
Page : 450 pages
File Size : 48,7 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:1137063894

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations by Anonim Pdf

Author : Claude Carasso,Pierre Charrier,Bernard Hanouzet,Jean-Luc Joly
Publisher : Springer
Page : 254 pages
File Size : 44,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468004

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Nonlinear Hyperbolic Problems by Claude Carasso,Pierre Charrier,Bernard Hanouzet,Jean-Luc Joly Pdf

The papers included in this proceedings volume are mostly original research papers, dealing with life-span of waves, nonlinear interaction of waves, and various applications to fluid mechanics.

Author : Tatsien Li,Yuejun Peng,Bopeng Rao
Publisher : World Scientific
Page : 464 pages
File Size : 40,8 Mb
Release : 2010-09-21
Category : Mathematics
ISBN : 9789814464048

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Some Problems On Nonlinear Hyperbolic Equations And Applications by Tatsien Li,Yuejun Peng,Bopeng Rao Pdf

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Author : R. Vichnevetsky,J. B. Bowles
Publisher : SIAM
Page : 146 pages
File Size : 49,5 Mb
Release : 1982-01-01
Category : Technology & Engineering
ISBN : 9780898713923

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Fourier Analysis of Numerical Approximations of Hyperbolic Equations by R. Vichnevetsky,J. B. Bowles Pdf

This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.

Author : Claude Carasso,Pierre-Arnaud Raviart,Denis Serre
Publisher : Springer
Page : 356 pages
File Size : 46,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478058

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Nonlinear Hyperbolic Problems by Claude Carasso,Pierre-Arnaud Raviart,Denis Serre Pdf

The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.

Author : Alfio Quarteroni,Alberto Valli
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 53,9 Mb
Release : 2008-09-24
Category : Mathematics
ISBN : 9783540852674

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Numerical Approximation of Partial Differential Equations by Alfio Quarteroni,Alberto Valli Pdf

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Author : Remi Abgrall,Chi-Wang Shu
Publisher : Elsevier
Page : 610 pages
File Size : 49,9 Mb
Release : 2017-01-16
Category : Mathematics
ISBN : 9780444639110

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Handbook of Numerical Methods for Hyperbolic Problems by Remi Abgrall,Chi-Wang Shu Pdf

Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage

Author : Giuseppe Geymonat
Publisher : World Scientific
Page : 196 pages
File Size : 51,7 Mb
Release : 1987
Category : Mathematics
ISBN : 9971502054

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Partial Differential Equations of Hyperbolic Type and Applications by Giuseppe Geymonat Pdf

This book introduces the general aspects of hyperbolic conservation laws and their numerical approximation using some of the most modern tools: spectral methods, unstructured meshes and ?-formulation. The applications of these methods are found in some significant examples such as the Euler equations. This book, a collection of articles by the best authors in the field, exposes the reader to the frontier of the research and many open problems.

Author : Remi Abgrall,Chi-Wang Shu
Publisher : Elsevier
Page : 666 pages
File Size : 48,8 Mb
Release : 2016-11-17
Category : Mathematics
ISBN : 9780444637956

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Handbook of Numerical Methods for Hyperbolic Problems by Remi Abgrall,Chi-Wang Shu Pdf

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications Written by leading subject experts in each field who provide breadth and depth of content coverage

Author : Michael Beals
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461245544

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Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by Michael Beals Pdf

This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 496 pages
File Size : 46,8 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 9781139434188

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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque Pdf

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Author : Jan S. Hesthaven
Publisher : SIAM
Page : 571 pages
File Size : 46,9 Mb
Release : 2018-01-30
Category : Science
ISBN : 9781611975093

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Numerical Methods for Conservation Laws by Jan S. Hesthaven Pdf

Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms: offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material are available online at www.siam.org/books/cs18.

Author : Peter D. Lax
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 49,5 Mb
Release : 2006
Category : Differential equations, Hyperbolic
ISBN : 9780821835760

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Hyperbolic Partial Differential Equations by Peter D. Lax Pdf

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. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Author : Jan S. Hesthaven,Sigal Gottlieb,David Gottlieb
Publisher : Cambridge University Press
Page : 4 pages
File Size : 44,6 Mb
Release : 2007-01-11
Category : Mathematics
ISBN : 9781139459525

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Spectral Methods for Time-Dependent Problems by Jan S. Hesthaven,Sigal Gottlieb,David Gottlieb Pdf

Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.