Automated solution of differential equations by the finite element method : the FEniCS book

Printed edition:

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 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 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 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 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