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A posteriori error estimation techniques for finite element methods

Author: Rüdiger Verfürth
Publisher: Oxford : Oxford University Press, 2013.
Series: Numerical mathematics and scientific computation.; Oxford science publications.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these  Read more...

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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Rüdiger Verfürth
ISBN: 9780199679423 0199679428
OCLC Number: 843345290
Notes: Formerly CIP.
Description: xx, 393 pages, 2 unnumbered pages of plates : illustrations (some color) ; 24 cm.
Contents: Machine generated contents note: 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-Smoothing --
2.4. 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. Poincare and Friedrichs' Inequalities --
3.5. Interpolation Error Estimates --
3.6. Inverse Estimates --
3.7. Decomposition of Affine Functions in LP (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 Equation --
4.9. 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 Equations --
6.6. Nonlinear Parabolic Equations of Second Order --
6.7. Finite Volume Methods --
6.8. Convergence of the Adaptive Process III.
Series Title: Numerical mathematics and scientific computation.; Oxford science publications.
Responsibility: Rüdiger Verfürth, Fakultät für Mathematik, Ruhr-Universität Bochum.
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Error control and adaptive solution algorithms for finite element approximation are a key concern of every practitioner. The present text, written by a leading authority in the field who has made Read more...

 
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