The Finite Element Method: Theory, Implementation, and Applications

Front Cover
Springer Science & Business Media, Jan 13, 2013 - Computers - 395 pages
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Chapter 1 Piecewise Polynomial Approximation in 1D
1
Chapter 2 The Finite Element Method in 1D
23
Chapter 3 Piecewise Polynomial Approximation in 2D
45
Chapter 4 The Finite Element Method in 2D
70
Chapter 5 TimeDependent Problems
113
Chapter 6 Solving Large Sparse Linear Systems
143
Chapter 7 Abstract Finite Element Analysis
177
Chapter 8 The Finite Element
202
Chapter 10 Transport Problems
240
Chapter 11 Solid Mechanics
257
Chapter 12 Fluid Mechanics
289
Chapter 13 Electromagnetics
326
Chapter 14 Discontinuous Galerkin Methods
355
Appendix A Some Additional Matlab Code
373
References
378
Index
382

Chapter 9 Nonlinear Problems
225

Other editions - View all

Common terms and phrases