Adaptive Finite Element Methods for Differential Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2003
|
| Series: | Lectures in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | These Lecture Notes discuss concepts of 'self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix. For the practical exercises, sample programs are provided via internet |
| Physical Description: | 1 Online-Ressource (VIII, 208 p) |
| ISBN: | 9783034876056 9783764370091 |
| DOI: | 10.1007/978-3-0348-7605-6 |
Staff View
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| 500 | |a These Lecture Notes discuss concepts of 'self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix. For the practical exercises, sample programs are provided via internet | ||
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034876056 9783764370091 |
| language | English |
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| spelling | Bangerth, Wolfgang Verfasser aut Adaptive Finite Element Methods for Differential Equations by Wolfgang Bangerth, Rolf Rannacher Basel Birkhäuser Basel 2003 1 Online-Ressource (VIII, 208 p) txt rdacontent c rdamedia cr rdacarrier Lectures in Mathematics These Lecture Notes discuss concepts of 'self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix. For the practical exercises, sample programs are provided via internet Mathematics Differential Equations Computer science / Mathematics Ordinary Differential Equations Computational Mathematics and Numerical Analysis Classical Continuum Physics Informatik Mathematik Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Finite-Elemente-Methode (DE-588)4017233-8 s Adaptives Verfahren (DE-588)4310560-9 s 1\p DE-604 Rannacher, Rolf Sonstige oth https://doi.org/10.1007/978-3-0348-7605-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bangerth, Wolfgang Adaptive Finite Element Methods for Differential Equations Mathematics Differential Equations Computer science / Mathematics Ordinary Differential Equations Computational Mathematics and Numerical Analysis Classical Continuum Physics Informatik Mathematik Differentialgleichung (DE-588)4012249-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Adaptives Verfahren (DE-588)4310560-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4017233-8 (DE-588)4310560-9 |
| title | Adaptive Finite Element Methods for Differential Equations |
| title_auth | Adaptive Finite Element Methods for Differential Equations |
| title_exact_search | Adaptive Finite Element Methods for Differential Equations |
| title_full | Adaptive Finite Element Methods for Differential Equations by Wolfgang Bangerth, Rolf Rannacher |
| title_fullStr | Adaptive Finite Element Methods for Differential Equations by Wolfgang Bangerth, Rolf Rannacher |
| title_full_unstemmed | Adaptive Finite Element Methods for Differential Equations by Wolfgang Bangerth, Rolf Rannacher |
| title_short | Adaptive Finite Element Methods for Differential Equations |
| title_sort | adaptive finite element methods for differential equations |
| topic | Mathematics Differential Equations Computer science / Mathematics Ordinary Differential Equations Computational Mathematics and Numerical Analysis Classical Continuum Physics Informatik Mathematik Differentialgleichung (DE-588)4012249-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Adaptives Verfahren (DE-588)4310560-9 gnd |
| topic_facet | Mathematics Differential Equations Computer science / Mathematics Ordinary Differential Equations Computational Mathematics and Numerical Analysis Classical Continuum Physics Informatik Mathematik Differentialgleichung Finite-Elemente-Methode Adaptives Verfahren |
| url | https://doi.org/10.1007/978-3-0348-7605-6 |
| work_keys_str_mv | AT bangerthwolfgang adaptivefiniteelementmethodsfordifferentialequations AT rannacherrolf adaptivefiniteelementmethodsfordifferentialequations |