Librería Portfolio

Table of Contents:
Preface -- List of Figures -- List of Tables -- 1. One-Dimensional Model Problems -- 1.1. Examples of one-dimensional problems -- 1.2. The finite element method -- 1.2.1. Basis (shape) functions -- 1.2.2. Linear systems -- 1.3. Boundary conditions -- 1.3.1. Nonhomogeneous Dirichlet boundary conditions -- 1.3.2. General boundary conditions -- 1.4. Local coordinate formulation -- 1.4.1. Element matrices -- 1.4.2. Local coordinate transformation -- 1.5. Computer programming considerations -- 1.6. Equivalence and error estimates -- 1.7. Exercises -- 2. Two-Dimensional Model Problems -- 2.1. Two-dimensional differential problems -- 2.2. The finite element method -- 2.2.1. Green´s formula -- 2.2.2. Variational formulation -- 2.2.3. Basis (shape) functions -- 2.2.4. Linear systems -- 2.3. Extensions to general boundary conditions -- 2.3.1. Nonhomogeneous Dirichlet boundary conditions -- 2.3.2. General boundary conditions -- 2.4. Local coordinate formulations -- 2.4.1. Local element matrices -- 2.4.2. Construction of triangulations -- 2.4.3. Assembly of stiffness matrices -- 2.4.4. Local coordinate transformation -- 2.5. Programming considerations -- 2.5.1. Numbering of nodes -- 2.5.2. Matrix storage -- 2.5.3. Computer program -- 2.6. Error estimates -- 2.7. Exercises -- 3. General Variational Formulatio -- 3.1. Continuous variational formulation -- 3.2. The finite element method -- 3.3. Examples -- 3.4. Exercises -- 4. One-Dimensional Elements and their Properties -- 4.1. Element classification -- 4.2. Different approaches for deriving basis functions -- 4.2.1. Global coordinate approach -- 4.2.2. Local coordinate transformation approach -- 4.2.3. Interpolation function approach -- 4.3. Lagrangian elements -- 4.4. Hermitian elements -- 4.5. Exercises -- 5. Two-Dimensional Elements and their Properties -- 5.1. Rectangular and´quadrilateral elements -- 5.1.1. Lagrangian rectangular elements -- 5.1.2. Serendipity elements -- 5.1.3. Hermitian rectangular elements -- 5.1.4. Quadrilateral elements -- 5.2. Triangular elements -- 5.2.1. Natural coordinates in two dimensions -- 5.2.2. Lagrangian triangular elements -- 5.2.3. Hermitian triangular elements -- 5.3. Exercises -- 6. Three-Dimensional Elements and their Properties -- 6.1. Hexahedral elements -- 6.1.1. Lagrangian hexahedral elements -- 6.1.2. Serendipity elements -- 6.2. Tetrahedral elements -- 6.2.1. Natural coordinates in three dimensions -- 6.2.2. Natural coordinates in d-dimensions -- 6.2.3. Lagrangian tetrahedral elements -- 6.2.4. Hermitian tetrahedral elements -- 6.3. Pentahedral elements -- 6.4. Isoparametric elements -- 6.5. Choice of an element -- 6.6. General domains -- 6.7. Quadrature rules -- 6.7.1. One dimension -- 6.7.2. Rectangles and bricks -- 6.7.3. Triangles and tetrahedra -- 6.8. Exercises -- 7. Finite Elements for Transient and Nonlinear Problems -- 7.1. Finite elements for transient problems -- 7.1.1. A one-dimensional model problem -- 7.1.2. A semi discrete scheme in space -- 7.1.3. Fully discrete schemes -- 7.2. Finite elements for nonlinear problems -- 7.2.1. Linearization approach -- 7.2.2. Extrapolation time approach -- 7.2.3. Implicit time approximation -- 7.2.4. Explicit time approximation -- 7.3. Exercises -- 8. Application to Solid Mechanics -- 8.1. Plane stress and plane strain -- 8.1.1. Kinematics -- 8.1.2. Equilibrium -- 8.1.3. Material laws -- 8.1.4. Boundary conditions -- 8.1.5. The finite element method -- 8.2. Three-dimensional solids -- 8.3. Axisymmetric solids -- 8.3.1. Anisotropic material -- 8.3.2. Isotropic material -- 8.4. Exercises -- 9. Application to Fluid Mechanics -- 9.1. Equations of fluid dynamics -- 9.2. A characteristic-based splitting method -- 9.2.1. An explicit characteristic-based method -- 9.2.2. Application to fluid mechanics -- 9.2.3. Solution schemes in time -- 9.2.4. Remarks on the splitting method -- 9.3. The finite element method -- 9.4. The nonconforming finite element method -- 9.5. The mixed finite element method -- 9.6. The Navier-Stokes equations -- 9.7. Exercises -- 10. Application to Porous Media Flow -- 10.1. Single-phase flow -- 10.1.1. Basic differential equations -- 10.1.2. Units -- 10.1.3. Different forms of flow equations -- 10.1.4. Boundary and initial conditions -- 10.2. Two-phase flow -- 10.2.1. Basic differential equations -- 10.2.2. Alternative differential equations -- 10.2.3. Boundary conditions -- 10.3. Finite element solution of single-phase flow -- 10.3.1. Treatment of initial conditions -- 10.3.2. The finite element method -- 10.3.3. Practical issues -- 10.4. Exercises -- 11. Other Finite Element Methods -- 11.1. The CVFE method -- 11.1.1. The basic CVFE method -- 11.1.2. Positive transmissibilities -- 11.1.3. The CVFE grid construction -- 11.1.4. Flux continuity -- 11.2. Multipoint flux approximations -- 11.2.1. Definition of MPFA -- 11.2.2. A-orthogonal grids -- 11.3. The nonconforming finite element method -- 11.3.1. Second-order partial differential problems -- 11.3.2. Nonconforming finite elements on triangles -- 11.4. The mixed finite element method -- 11.4.1. A one-dimensional model problem -- 11.4.2. A two-dimensional model problem -- 11.4.3. Extension to boundary conditions for other Kids -- 11.4.4. Mixed finite element spaces -- 11.5. The discontinuous finite element method -- 11.5.1. DG methods -- 11.5.2. Stabilized DG methods -- 11.6. The characteristic finite element method -- 11.6.1. The modified method of characteristics -- 11.6.2. The Eulerian-Lagrangian localized adjoint method -- 11.7. The adaptive finite element method -- 11.7.1. Local grid refinement in space -- 11.7.2. Data structures -- 11.7.3. A posteriori error estimates -- 11.8. The multiscale finite element method -- 11.8.1. The multiscale finite element method -- 11.8.2. Boundary conditions of basis functions -- 11.9. Exercises -- Bibliography -- Index.