A posteriori error estimation techniques for finite element methods:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford, UK
Oxford University Press
2013
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| Schriftenreihe: | Numerical mathematics and scientific computation
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 developing self-adaptive discretization methods 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. Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (xviii, 393 pages) |
| ISBN: | 0191668761 019166877X 0191758485 0199679428 9780191668760 9780191668777 9780191758485 9780199679423 |
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| 500 | |a 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 developing self-adaptive discretization methods | ||
| 500 | |a 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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. | ||
| 500 | |a Includes bibliographical references and index | ||
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| id | DE-604.BV043055489 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:06Z |
| institution | BVB |
| isbn | 0191668761 019166877X 0191758485 0199679428 9780191668760 9780191668777 9780191758485 9780199679423 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028479680 |
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| spelling | Verfürth, Rüdiger Verfasser aut A posteriori error estimation techniques for finite element methods Rüdiger Verfürth Oxford, UK Oxford University Press 2013 1 Online-Ressource (xviii, 393 pages) txt rdacontent c rdamedia cr rdacarrier Numerical mathematics and scientific computation 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 developing self-adaptive discretization methods 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. Includes bibliographical references and index MATHEMATICS / Numerical Analysis bisacsh Finite element method fast Finite element method Fehlerabschätzung (DE-588)4228085-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Fehlerabschätzung (DE-588)4228085-0 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=551490 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Verfürth, Rüdiger A posteriori error estimation techniques for finite element methods MATHEMATICS / Numerical Analysis bisacsh Finite element method fast Finite element method Fehlerabschätzung (DE-588)4228085-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4228085-0 (DE-588)4017233-8 |
| title | A posteriori error estimation techniques for finite element methods |
| title_auth | A posteriori error estimation techniques for finite element methods |
| title_exact_search | A posteriori error estimation techniques for finite element methods |
| title_full | A posteriori error estimation techniques for finite element methods Rüdiger Verfürth |
| title_fullStr | A posteriori error estimation techniques for finite element methods Rüdiger Verfürth |
| title_full_unstemmed | A posteriori error estimation techniques for finite element methods Rüdiger Verfürth |
| title_short | A posteriori error estimation techniques for finite element methods |
| title_sort | a posteriori error estimation techniques for finite element methods |
| topic | MATHEMATICS / Numerical Analysis bisacsh Finite element method fast Finite element method Fehlerabschätzung (DE-588)4228085-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | MATHEMATICS / Numerical Analysis Finite element method Fehlerabschätzung Finite-Elemente-Methode |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=551490 |
| work_keys_str_mv | AT verfurthrudiger aposteriorierrorestimationtechniquesforfiniteelementmethods |