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**Automated solution of differential equations by the finite element method. The FEniCS book.**
*(English)*
Zbl 1247.65105

Lecture Notes in Computational Science and Engineering 84. Berlin: Springer (ISBN 978-3-642-23098-1/hbk; 978-3-642-23099-8/ebook). xiii, 723 p. (2012).

This book is written by researchers behind the FEniCS Project, a project set out in 2003 with an idea to automate the solution of mathematical models based on differential equations. The presentation spans mathematical background, software design and the use of FEniCS in applications.

The book begins with a tutorial for readers who are new to the topic. Following the tutorial, chapters in Part I address fundamental aspects of the approach to automating the creation of finite element solvers. The implementation of central components is described in Part II, while Part III concerns a wide range of applications, including fluid flow, solid mechanics, electromagnetism and geophysics.

Some of the chapters in this book are accompanied by supplementary material in the form of code examples.

The software developed by the FEniCS Project is free for all to use and modify and so is this book. Permission is granted to copy, distribute and/or modify this book under the terms of the “GNU Free Documentation License” a copy of this license being included in the chapter with the same title.

The book begins with a tutorial for readers who are new to the topic. Following the tutorial, chapters in Part I address fundamental aspects of the approach to automating the creation of finite element solvers. The implementation of central components is described in Part II, while Part III concerns a wide range of applications, including fluid flow, solid mechanics, electromagnetism and geophysics.

Some of the chapters in this book are accompanied by supplementary material in the form of code examples.

The software developed by the FEniCS Project is free for all to use and modify and so is this book. Permission is granted to copy, distribute and/or modify this book under the terms of the “GNU Free Documentation License” a copy of this license being included in the chapter with the same title.

Reviewer: Titus Petrila (Cluj-Napoca)

### MSC:

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

65Y15 | Packaged methods for numerical algorithms |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

76M10 | Finite element methods applied to problems in fluid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |

86-08 | Computational methods for problems pertaining to geophysics |

65-06 | Proceedings, conferences, collections, etc. pertaining to numerical analysis |

00B15 | Collections of articles of miscellaneous specific interest |