Overview
- 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
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 fewbasic results from linear algebra, geometry, and mathematical and numerical analysis.
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Simplicial Partitions with Applications to the Finite Element Method
Authors: Jan Brandts, Sergey Korotov, Michal Křížek
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-55677-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-55676-1Published: 06 October 2020
Softcover ISBN: 978-3-030-55679-2Published: 07 October 2021
eBook ISBN: 978-3-030-55677-8Published: 05 October 2020
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XV, 188
Number of Illustrations: 92 b/w illustrations, 10 illustrations in colour
Topics: Numerical Analysis, Applications of Mathematics, Analysis, Math. Applications in Chemistry