Overview
- Provides application orientated introduction to the numerical methods for partial differential equations
- Examines modern topics, including cell-centered finite volume methods and methods of convection-dominated problems
- Includes detailed illustrations and extensive exercises throughout
Part of the book series: Texts in Applied Mathematics (TAM, volume 44)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
- finite element method
- finite volume method
- finite difference method
- mixed methods
- nonconforming methods
- elliptic boundary value problems
- parabolic initial boundary value problems
- diffusion-convection-reaction equation
- discontinuous Galerkin method
- iterative methods for sparse systems of linear equations
- grid generation and adaptation
About this book
This second edition sees additional chapters on mixed discretization and on generalizing and unifying known approaches; broader applications on systems of diffusion, convection and reaction; enhanced chapters on node-centered finite volume methods and methods of convection-dominated problems, specifically treating the now-popular cell-centered finite volume method; and the consideration of realistic formulations beyond the Poisson's equation for all models and methods.
Reviews
“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)
“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)
Authors and Affiliations
About the authors
After the study of Mathematics and Computer Science at the Freie Universität Berlin (diploma in 1972) he earned a PhD from the University of Augsburg in 1983, where he also received a higher doctoral degree (habilitation) in 1988.
Peter Knabner is author of more than 180 peer-reviewed publications in applied analysis, numerical mathematics and geohydrology. He is author and co-author of 13 research monographs and textbooks in German and English.
Lutz Angermann is Professor of Numerical Mathematics at the Department of Mathematics of the Clausthal University of Technology since 2001. His research is concerned with the development and mathematical analysis of numerical methods for solving partial differential equations with special interests in finite volume and finite element methods and their application to problems in Physics and Engineering.
After the study of Mathematics at the State University of Kharkov (now V.N. Karazin Kharkiv National University, Ukraine) he earned a PhD from the University of Technology at Dresden in 1987. The University of Erlangen-Nürnberg awarded him a higher doctoral degree (habilitation) in 1995. From 1998 to 2001, he held the post of an Associate Professor of Numerical Mathematics at the University of Magdeburg.
He has authored or co-authored about 100 scientific papers, among them four books as co-author, and he edited two books.
Bibliographic Information
Book Title: Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Book Subtitle: With contributions by Andreas Rupp
Authors: Peter Knabner, Lutz Angermann
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-3-030-79385-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-79384-5Published: 20 November 2021
Softcover ISBN: 978-3-030-79387-6Published: 21 November 2022
eBook ISBN: 978-3-030-79385-2Published: 19 November 2021
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 2
Number of Pages: XIX, 802
Number of Illustrations: 96 b/w illustrations, 2 illustrations in colour
Topics: Numerical Analysis, Analysis, Applications of Mathematics, Computational Mathematics and Numerical Analysis, Numerical and Computational Physics, Simulation, Mathematical and Computational Engineering