This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Author(s): Langtangen, Mardal
Series: Texts in Computational Science and Engineering
Edition: 1
Publisher: Springer
Year: 2019
Language: English
Pages: 405
Front Matter ....Pages i-xvi
Quick Overview of the Finite Element Method (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 1-6
Function Approximation by Global Functions (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 7-68
Function Approximation by Finite Elements (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 69-129
Variational Formulations with Global Basis Functions (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 131-171
Variational Formulations with Finite Elements (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 173-231
Time-Dependent Variational Forms (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 233-257
Variational Forms for Systems of PDEs (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 259-280
Flexible Implementations of Boundary Conditions (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 281-298
Nonlinear Problems (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 299-364
Variational Methods for Linear Systems (Hans Petter Langtangen, Kent-Andre Mardal)....Pages 365-376
Back Matter ....Pages 377-395
