Adaptive finite element methods for differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2003
|
| Series: | Lectures in mathematics : ETH Zürich
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 207 S. Ill., graph. Darst. |
| ISBN: | 3764370092 |
Staff View
MARC
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| 245 | 1 | 0 | |a Adaptive finite element methods for differential equations |c Wolfgang Bangerth ; Rolf Rannacher |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Introduction 1
1.1 A first example: computation of drag coefficient 2
1.2 The need for goal oriented mesh adaptation 4
1.3 Further examples of goal oriented simulation 9
1.4 General concepts of error estimation 11
2 An ODE Model Case 15
2.1 Finite differences and finite elements 15
2.2 Efficiency comparison: FD versus FE method 19
2.3 Exercises 23
3 A PDE Model Case 25
3.1 Finite element approximation 26
3.2 Global a posteriori error estimates 29
3.3 A posteriori error estimates for output functionals 30
3.4 Higher order finite elements 37
3.5 Exercises 39
4 Practical Aspects 41
4.1 Evaluation of the error identity and indicators 42
4.2 Mesh adaptation 46
4.3 Use of error estimators for post processing 52
4.4 Towards anisotropic mesh adaptation 55
4.5 Exercises 60
5 The Limits of Theoretical Analysis 61
5.1 Convergence of residuals 64
5.2 Approximation of weights 65
5.3 Exercises 69
vi Contents
6 An Abstract Approach for Nonlinear Problems 71
6.1 Galerkin approximation of nonlinear equations 72
6.2 A nested solution approach 78
6.3 Exercises 79
7 Eigenvalue Problems 81
7.1 A posteriori error analysis . 82
7.2 Error control for functionals of eigenfunctions 91
7.3 The stability eigenvalue problem 95
7.4 Exercises 99
8 Optimization Problems 101
8.1 A posteriori error analysis via Lagrange formalism 103
8.2 Application to a boundary control problem 105
8.3 Application to parameter estimation . 110
8.4 Exercises 111
9 Time Dependent Problems 113
9.1 Galerkin discretization 113
9.2 A parabolic model problem: the heat equation 115
9.3 A hyperbolic model problem: the wave equation 123
9.4 Exercises 128
10 Applications in Structural Mechanics 129
10.1 Approximation of the Lame Navier system 129
10.2 A model problem in elasto plasticity theory 134
10.3 Exercises 142
11 Applications in Fluid Mechanics 143
11.1 Computation of drag and lift in a viscous flow 144
11.2 Minimization of drag by boundary control 152
11.3 Stability analysis for stationary flow . 156
11.4 Exercises 160
12 Miscellaneous and Open Problems 161
12.1 Some historical remarks 161
12.2 Current developments 162
12.3 Open problems 164
A Solutions of exercises 167
Bibliography 191
Index 203
|
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| indexdate | 2024-07-09T19:11:31Z |
| institution | BVB |
| isbn | 3764370092 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010211517 |
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| physical | VIII, 207 S. Ill., graph. Darst. |
| publishDate | 2003 |
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| series2 | Lectures in mathematics : ETH Zürich |
| spelling | Bangerth, Wolfgang 1973- Verfasser (DE-588)1146171307 aut Adaptive finite element methods for differential equations Wolfgang Bangerth ; Rolf Rannacher Basel [u.a.] Birkhäuser 2003 VIII, 207 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics : ETH Zürich Éléments finis, Méthode des Équations différentielles - Solutions numériques Differential equations Numerical solutions Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Finite-Elemente-Methode (DE-588)4017233-8 s Adaptives Verfahren (DE-588)4310560-9 s DE-604 Rannacher, Rolf 1948- Verfasser (DE-588)108664732 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bangerth, Wolfgang 1973- Rannacher, Rolf 1948- Adaptive finite element methods for differential equations Éléments finis, Méthode des Équations différentielles - Solutions numériques Differential equations Numerical solutions Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd Adaptives Verfahren (DE-588)4310560-9 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4310560-9 (DE-588)4012249-9 |
| 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 Wolfgang Bangerth ; Rolf Rannacher |
| title_fullStr | Adaptive finite element methods for differential equations Wolfgang Bangerth ; Rolf Rannacher |
| title_full_unstemmed | Adaptive finite element methods for differential equations Wolfgang Bangerth ; Rolf Rannacher |
| title_short | Adaptive finite element methods for differential equations |
| title_sort | adaptive finite element methods for differential equations |
| topic | Éléments finis, Méthode des Équations différentielles - Solutions numériques Differential equations Numerical solutions Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd Adaptives Verfahren (DE-588)4310560-9 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Éléments finis, Méthode des Équations différentielles - Solutions numériques Differential equations Numerical solutions Finite element method Finite-Elemente-Methode Adaptives Verfahren Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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