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Springer Monographs in Mathematics

Simplicial Partitions with Applications to the Finite Element Method

Authors: Brandts, Jan, Korotov, Sergey, Křížek, Michal

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  • Provides an accessible introduction to the finite element method (FEM), requiring only minimal prerequisites
  • Emphasizes angle conditions for FEM convergence for elliptic PDEs with boundary conditions
  • Presents 0/1-simplicial partitions of higher-dimensional unit cubes and maximally symmetric manifolds
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eBook 85,59 €
price for Spain (gross)
  • ISBN 978-3-030-55677-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
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Hardcover 103,99 €
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About this book

This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields.
These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions. 
It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis. 

About the authors

Assoc. Prof. Jan Brandts is the director of Mathematics and Computer Science at the Faculty of Science, University of Amsterdam. For five years he was the Editor-in-Chief of the Springer journal Applications of Mathematics.  
Prof. Sergey Korotov is a senior researcher and lecturer at the Western Norway University in Bergen. 
Prof. Michal Krizek is the head of the Numerical Analysis Department of the Institute of Mathematics of the Czech Academy of Sciences. For many years he was Editor-in-Chief of the Czech journal Advances of Mathematics, Physics and Astronomy, and the journal Applications of Mathematics. He is a member of the Czech Learned Society and is the author or coauthor of a wide range of monographs. All three authors have a common interest in numerical analysis, the finite element method for solving partial differential equations, mathematical physics, linear algebra, and mathematical and functional analysis.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook 85,59 €
price for Spain (gross)
  • ISBN 978-3-030-55677-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Simplicial Partitions with Applications to the Finite Element Method
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-55677-8
DOI
10.1007/978-3-030-55677-8
Hardcover ISBN
978-3-030-55676-1
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XV, 188
Number of Illustrations
92 b/w illustrations, 10 illustrations in colour
Topics