Overview
- The review on central schemes, on error estimates for discontinuous Galerkin methods and on the use of wavelets in scientific computing form an excellent teaching material for graduate students
- Includes supplementary material: sn.pub/extras
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (15 chapters)
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Front Matter
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Wavelets and Partial Differential Equations
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Front Matter
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Back Matter
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High-Order Shock-Capturing Schemes for Balance Laws
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Front Matter
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Back Matter
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Discontinuous Galerkin Methods: General Approach and Stability
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Front Matter
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Keywords
About this book
This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical techniques.
The book has three parts. The first one is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of writing equivalent norms for the scale of Besov spaces allows to develop some new methods. The second part provides an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws, with emphasis on providing a unified view of such schemes by identifying the essential aspects of their construction. In the last part a general introduction is given to the discontinuous Galerkin methods for solving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates.
Reviews
From the reviews:
“It includes an extended version of the lectures given by the four authors at the Advanced School on Numerical Solutions of Partial Differential Equations: New Trends and Applications, held at the CRM – Barcelona between November 15 – 22, 2007. … The book is addressed to masterands, for PhD candidates and to research workers in the fields of applied mathematics and engineering.” (Constantin I. Popovici, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)
“The book is well written and organized at a difficulty level that precisely meets the target audiences’ needs. … PhD students as well as engineers and researchers in the field of applied mathematics or scientific computing and interested graduate students will find this book an excellent resource to rapid introduction into the field of modern numerical methods … . serve as a textbook for graduate – level courses in numerical methods … . be useful for experienced researchers and practitioners both from academia or industry.” (Andrzej Myśliński, Control and Cybernetics, Vol. 39 (3), 2010)Authors and Affiliations
Bibliographic Information
Book Title: Numerical Solutions of Partial Differential Equations
Authors: Silvia Bertoluzza, Giovanni Russo, Silvia Falletta, Chi-Wang Shu
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-7643-8940-6
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2009
Softcover ISBN: 978-3-7643-8939-0Published: 10 December 2008
eBook ISBN: 978-3-7643-8940-6Published: 13 March 2009
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: X, 202