Authors:
- Understanding the mathematical foundations helps the reader design methods for new applications
- Bridging the gap between finite volumes, finite elements, and discontinuous Galerkin methods provides new insight on numerical methods
- The mathematical setting for the continuous model is a key to successful approximation methods
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathématiques et Applications (MATHAPPLIC, volume 69)
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Table of contents (7 chapters)
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Front Matter
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Scalar First-Order PDEs
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Front Matter
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Scalar first order PDEs
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Scalar Second-Order PDEs
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Front Matter
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Scalar second order PDEs
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Systems
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Front Matter
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Back Matter
About this book
Reviews
From the reviews:
“The goal of this book is to provide graduate students and researchers in numerical methods with the basic mathematical concepts to design and analyze discontinuous Galerkin (DG) methods for various model problems, starting at an introductory level and further elaborating on more advanced topics, considering that DG methods have tremendously developed in the last decade.” (Rémi Vaillancourt, Mathematical Reviews, January, 2013)
“The book is structured in three parts: scalar first order PDEs, scalar second order PDEs, and systems. … For researchers in numerical analysis it is nice to see that for all problem classes the authors start with a full analysis of existence, uniqueness, and properties of the solution of the continuous problem. … this new monograph is an extremely valuable source concerning the theoretical function of dG methods for the advanced reader.” (H.-G. Roos, SIAM Review, Vol. 55 (2), 2013)
“This new monograph is an extremely valuable collection of the mathematical treatment of discontinuous Galerkin methods with 300 references and providing profound insight into the required techniques. It collects and presents also several recent results for elliptic and non-elliptic, stationary and non-stationary partial differential equations in a unified framework. Thus it is strongly recommendable for researchers in the field.” (Christian Wieners, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 92 (7), 2012)
“The aim of the book is ‘to provide the reader with the basic mathematical concepts to design and analyze discontinuous Galerkin methods for various model problems, starting at an introductory level and further elaborating on more advanced topics’. … Some useful practical implementation aspects are considered in an Appendix. The bibliography contains more than 300 entries.” (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1231, 2012)
Authors and Affiliations
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, Department of Applied Mathematics, IFP Energies nouvelles, Rueil-Malmaison, France
Daniele Antonio Di Pietro
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, CERMICS, Ecole des Ponts ParisTech, Université Paris Est, Marne la Vallée cedex 2, France
Alexandre Ern
Bibliographic Information
Book Title: Mathematical Aspects of Discontinuous Galerkin Methods
Authors: Daniele Antonio Di Pietro, Alexandre Ern
Series Title: Mathématiques et Applications
DOI: https://doi.org/10.1007/978-3-642-22980-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Softcover ISBN: 978-3-642-22979-4Published: 04 November 2011
eBook ISBN: 978-3-642-22980-0Published: 03 November 2011
Series ISSN: 1154-483X
Series E-ISSN: 2198-3275
Edition Number: 1
Number of Pages: XVII, 384
Number of Illustrations: 34 b/w illustrations
Topics: Numerical Analysis, Computational Mathematics and Numerical Analysis, Mathematical and Computational Engineering