Property-Preserving Numerical Schemes for Conservation Laws
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Book Overview High-order numerical methods for hyperbolic conservation laws do not guarantee the validity of constraints that physically meaningful app...
High-order numerical methods for hyperbolic conservation laws do not guarantee the validity of constraints that physically meaningful approximations are supposed to satisfy. The finite volume and finite element schemes summarized in this book use limiting techniques to enforce discrete maximum principles and entropy inequalities. Spurious oscillations are prevented using artificial viscosity operators and/or essentially nonoscillatory reconstructions.
An introduction to classical nonlinear stabilization approaches is given in the simple context of one-dimensional finite volume discretizations. Subsequent chapters of Part I are focused on recent extensions to continuous and discontinuous Galerkin methods. Many of the algorithms presented in these chapters were developed by the authors and their collaborators. Part II gives a deeper insight into the mathematical theory of property-preserving numerical schemes. It begins with a review of the convergence theory for finite volume methods and ends with analysis of algebraic flux correction schemes for finite elements. In addition to providing ready-to-use algorithms, this text explains the design principles behind such algorithms and shows how to put theory into practice. Although the book is based on lecture notes written for an advanced graduate-level course, it is also aimed at senior researchers who develop and analyze numerical methods for hyperbolic problems.
Book Details Format: Hardcover | Pages: 470 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9811278180
FormatHardcover
Pages470
LanguageEnglish
ISBN9811278180
EAN9789811278181
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date1970-01-01
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight1.81 Pounds
Length9.0 Inches
Width6.0 Inches
Height1.06 Inches
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