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A posteriori error estimation techniques for finite element methods /
A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This text gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford, UK :
Oxford University Press,
2013.
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| Colección: | Numerical mathematics and scientific computation.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; 1 A Simple Model Problem; 1.1 Motivation and Overview; 1.2 The Model Problem and its Discretisation; 1.3 Notations and Auxiliary Results; 1.4 Residual Estimates; 1.5 A Vertex-Oriented Residual Error Indicator; 1.6 Edge Residuals; 1.7 Auxiliary Local Problems; 1.8 A Hierarchical Approach; 1.9 Gradient Recovery; 1.10 Equilibrated Residuals; 1.11 Dual Weighted Residuals; 1.12 The Hyper-Circle Method; 1.13 Efficiency and Asymptotic Exactness; 1.14 Convergence of the Adaptive Process I; 1.15 Summary and Outlook; 2 Implementation; 2.1 Mesh-Refinement; 2.2 Mesh-Coarsening.
- 2.3 Mesh-Smoothing2.4 Data Structures; 2.5 Numerical Examples; 3 Auxiliary Results; 3.1 Function Spaces; 3.2 Finite Element Meshes and Spaces; 3.3 Trace Inequalities; 3.4 Poincaré and Friedrichs' Inequalities; 3.5 Interpolation Error Estimates; 3.6 Inverse Estimates; 3.7 Decomposition of Affine Functions in L[sup(p)] (0, 1; Y*); 3.8 Estimation of Residuals; 4 Linear Elliptic Equations; 4.1 Abstract Linear Problems; 4.2 The Model Problem Revisited; 4.3 Reaction-Diffusion Equations; 4.4 Convection-Diffusion Equations; 4.5 Anisotropic Meshes; 4.6 Non-Smooth Coefficients; 4.7 Eigenvalue Problems.
- 4.8 Mixed Formulation of the Poisson Equation4.9 The Equations of Linear Elasticity; 4.10 The Stokes Equations; 4.11 The Bi-harmonic Equation; 4.12 Non-Conforming Discretisations; 4.13 Convergence of the Adaptive Process II; 5 Nonlinear Elliptic Equations; 5.1 Abstract Nonlinear Problems; 5.2 Quasilinear Equations of Second Order; 5.3 Eigenvalue Problems Revisited; 5.4 The Stationary Navier-Stokes Equations; 6 Parabolic Equations; 6.1 The Heat Equation; 6.2 Time-Dependent Convection-Diffusion Equations; 6.3 Linear Parabolic Equations of Second Order; 6.4 The Method of Characteristics.
- 6.5 The Time-Dependent Stokes Equations6.6 Nonlinear Parabolic Equations of Second Order; 6.7 Finite Volume Methods; 6.8 Convergence of the Adaptive Process III; References; List of Symbols; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Y; Z.