| Description |
1 online resource (xiii, 723 pages) |
| Series |
Lecture notes in computational science and engineering, 1439-7358 ; 84 |
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Lecture notes in computational science and engineering ; 84.
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| Contents |
Automated Solution of Differential Equations by the Finite Element Method; The FEniCS Book; Preface; Contents; 1 A FEniCS tutorial; 1.1 Fundamentals; 1.1.1 The Poisson equation; 1.1.2 Variational formulation; 1.1.3 Implementation; 1.1.4 Controlling the solution process; 1.1.5 Linear variational problem and solver objects; 1.1.6 Examining the discrete solution; 1.1.7 Solving a real physical problem; 1.1.8 Quick visualization with VTK; 1.1.9 Computing derivatives; 1.1.10 A variable-coefficient Poisson problem; 1.1.11 Computing functionals; 1.1.12 Visualization of structured mesh data |
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1.1.13 Combining Dirichlet and Neumann conditions1.1.14 Multiple Dirichlet conditions; 1.1.15 A linear algebra formulation; 1.1.16 Parameterizing the number of space dimensions; 1.2 Nonlinear problems; 1.2.1 Picard iteration; 1.2.2 A Newton method at the algebraic level; 1.2.3 A Newton method at the PDE level; 1.2.4 Solving the nonlinear variational problem directly; 1.3 Time-dependent problems; 1.3.1 A diffusion problem and its discretization; 1.3.2 Implementation; 1.3.3 Avoiding assembly; 1.3.4 A physical example; 1.4 Creating more complex domains; 1.4.1 Built-in mesh generation tools |
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1.4.2 Transforming mesh coordinates1.5 Handling domains with different materials; 1.5.1 Working with two subdomains; 1.5.2 Implementation; 1.5.3 Multiple Neumann, Robin, and Dirichlet conditions; 1.6 More examples; 1.7 Miscellaneous topics; 1.7.1 Glossary; 1.7.2 Overview of objects and functions; 1.7.3 User-defined functions; 1.7.4 Linear solvers and preconditioners; 1.7.5 Installing FEniCS; 1.7.6 Books on the finite element method; 1.7.7 Books on Python; PartI Methodology; 2 The finite element method; 2.1 A simple model problem; 2.2 Finite element discretization |
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2.2.1 Discretizing Poisson's equation2.2.2 Discretizing the first-order system; 2.3 Finite element abstract formalism; 2.3.1 Linear problems; 2.3.2 Nonlinear problems; 2.4 Finite element function spaces; 2.4.1 The mesh; 2.4.2 The finite element definition; 2.4.3 The nodal basis; 2.4.4 The local-to-global mapping; 2.4.5 The global function space; 2.4.6 The mapping from the reference element; 2.5 Finite element solvers; 2.6 Finite element error estimation and adaptivity; 2.6.1 A priori error analysis; 2.6.2 A posteriori error analysis; 2.6.3 Adaptivity; 2.7 Automating the finite element method |
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2.8 Historical notes3 Common and unusual finite elements; 3.1 The finite element definition; 3.2 Notation; 3.3 H1 finite elements; 3.3.1 The Lagrange element; 3.3.2 The Crouzeix-Raviart element; 3.4 H(div) finite elements; 3.4.1 The Raviart-Thomas element; 3.4.2 The Brezzi-Douglas-Marini element; 3.4.3 The Mardal-Tai-Winther element; 3.4.4 The Arnold-Winther element; 3.5 H(curl) finite elements; 3.5.1 The Nédélec H(curl) element of the first kind; 3.5.2 The H(curl) Nédélec element of the second kind; 3.6 L2 finite elements; 3.6.1 Discontinuous Lagrange; 3.7 H2 finite elements |
| Summary |
This book is written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. 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. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics |
| Analysis |
Computer science |
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Computer software |
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Engineering mathematics |
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Mathematical Software |
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Theoretical, Mathematical and Computational Physics |
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Numeric Computing |
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Appl. Mathematics/Computational Methods of Engineering |
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Computational Science and Engineering |
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Earth Sciences, general |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Finite element method.
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Differential equations -- Numerical solutions -- Data processing
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Geography.
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Mathematics.
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Geography
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Mathematics
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Electronic Data Processing
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geography.
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Método de elementos finitos
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Ecuaciones diferenciales -- Soluciones numéricas
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Geografía
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Matemáticas
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Mathematics
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Geography
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Differential equations -- Numerical solutions -- Data processing
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Finite element method
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| Genre/Form |
Software.
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| Form |
Electronic book
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| Author |
Logg, Anders.
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Mardal, Kent-Andre.
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Wells, Garth, 1965-
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| ISBN |
9783642230998 |
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3642230997 |
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3642230989 |
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9783642230981 |
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