Simplicial Partitions with Applications to the Finite Element Method

by Jan Brandts, Sergey Korotov, Michal Krïzek

Overview

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 fewbasic results from linear algebra, geometry, and mathematical and numerical analysis.

Product Details

ISBN-13:	9783030556792
Publisher:	Springer International Publishing
Publication date:	10/06/2020
Series:	Springer Monographs in Mathematics
Edition description:	1st ed. 2020
Pages:	188
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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

Preface.- 1 Introduction. - 2 Simplices: Definitions and Properties. - 3 Simplicial Partitions. - 4 Angle Conditions. - 5 Nonobtuse Simplicial Partitions. - 6 Nonexistence of Acute Simplicial Partitions in R5. - 7 Tight Bounds on Angle Sums of Simplices. - 8 Refnement Techniques. - 9 The Discrete Maximum Principle. - 10 Variational Crimes. - 11 0/1-Simplices and 0/1-Triangulations. - 12 Tessellations of Maximally Symmetric Manifolds. - References. - Name Index. - Subject Index.