Theory and Practice of Finite Elements

✍ Scribed by Alexandre Ern, Jean-Luc Guermond (auth.)

• Publisher: Springer-Verlag New York
• Year: 2004
• Tongue: English
• Leaves: 530
• Series: Applied Mathematical Sciences 159
• Edition: 1
• Category: Library

✦ Synopsis

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation.

The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code.

Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences.

The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Finite Element Interpolation....Pages 3-80
Approximation in Banach Spaces by Galerkin Methods....Pages 81-108
Front Matter....Pages 109-109
Coercive Problems....Pages 111-174
Mixed Problems....Pages 175-217
First-Order PDEs....Pages 219-278
Time-Dependent Problems....Pages 279-334
Front Matter....Pages 335-335
Data Structuring and Mesh Generation....Pages 337-356
Quadratures, Assembling, and Storage....Pages 357-382
Linear Algebra....Pages 383-419
A Posteriori Error Estimates and Adaptive Meshes....Pages 421-460
Back Matter....Pages 461-526

✦ Subjects

Applications of Mathematics; Math Applications in Computer Science; Partial Differential Equations; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Mechanical Engineering