Simplicial Partitions with Applications to the Finite Element Method

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. 

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.