Authors:
- Self-contained introduction to discontinuous Galerkin methods
- Extensive discussion on computer implementation of the methods presented
- Cutting edge extensions of the very popular discontinuous Galerkin methods, explained in detail
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages.
This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen
t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.Reviews
“This book should be very useful to Ph.D students and researchers who are eager to explore and understand the mathematical analysis of DGFEMs on polytopic meshes for second-order elliptic equations. The presentation is lucid and the book provides an extensive list of references in the area.” (Neela Nataraj, Mathematical Reviews, October, 2018)
Authors and Affiliations
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Department of Mathematics, University of Leicester, Leicester, United Kingdom
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis
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School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
Paul Houston
Bibliographic Information
Book Title: hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Authors: Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-67673-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-67671-5Published: 07 December 2017
eBook ISBN: 978-3-319-67673-9Published: 27 November 2017
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: VIII, 131
Number of Illustrations: 31 b/w illustrations, 1 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Mathematics of Computing, Theoretical, Mathematical and Computational Physics