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Huang, Weizhang; Russell, Robert D.

Adaptive Moving Mesh Methods (Gebundene Ausgabe)

Reihe: Applied Marketing Science / Angewandte Marketingforschung 174

Springer-Verlag GmbH, Springer US, New York, N.Y., Dezember 2010

434 S. - Sprache: Englisch - 114 schwarz-weiße und 7 farbige Abbildungen - 249x164x29 mm

ISBN: 1441979158 EAN: 9781441979155

This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems.  Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book. 

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First ever comprehensive treatment of moving mesh methods for solving time-dependent Partial Differential EquationsGeneral error analysis for adaptive mesh generation using equidistribution and alignment is coveredNumerous numerical examples and several Matlab codes are included


Preface.- Introduction.- Adaptive Mesh Movement in 1D.- Discretization of PDEs on Time-Varying Meshes.- Basic Principles of Multidimensional Mesh Adaption.- Monitor Functions.- Variational Mesh Adaptive Methods.- Velocity-Based Adaptive Methods.- Appendix: Sobolev Spaces.- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality.- Bibliography.


From the reviews: "The book's focus is on mesh generation and adaptation through mesh movement techniques ... . is completed by an extensive bibliographical list consisting of more than 300 references. ... this has helped to fill in the gap between the practitioner's moving mesh techniques and a sound theoretical background. It is highly accessible and is characterized by a very clear and readable style without sacrificing mathematical rigor and soundness. ... a precious reference for a broad community of numerical analysts as well as for computational scientists."­­­ (Alfio Quarteroni, SIAM Review, Vol. 53 (4), 2011) "This book is valuable for both researchers and practitioners working in adaptive moving mesh methods. It presents unified analytical tools and implementation details, and provides applications of the adaptive moving mesh methods. ... In addition, the book can be used as a textbook for an advanced course in the numerical solution of partial differential equations." (Tsu-Fen Chen, Mathematical Reviews, Issue 2012 a) "This advanced textbook on adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations (mostly of parabolic type) is aimed at graduate students and researchers in the field of scientific computing and numerical analysis. ... The book is illustrated with numerous examples, which have been implemented in Matlab." (Kai Schneider, Zentralblatt MATH, Vol. 1227, 2012)

ISBN 1-441979-15-8, ISBN 1-44-197915-8, ISBN 1-44197-915-8, ISBN 1-441-97915-8, ISBN 1-4419-7915-8

ISBN 978-1-441979-15-5, ISBN 978-1-44-197915-5, ISBN 978-1-44197-915-5, ISBN 978-1-441-97915-5, ISBN 978-1-4419-7915-5

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