Adaptive monotone multigrid methods for nonlinear variational problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
Stuttgart
Teubner
1997
|
| Edition: | 1. Aufl. |
| Series: | Advances in numerical mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 157 S. graph. Darst. |
| ISBN: | 3519027224 |
Staff View
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| 245 | 1 | 0 | |a Adaptive monotone multigrid methods for nonlinear variational problems |c von Ralf Kornhuber |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Stuttgart |b Teubner |c 1997 | |
| 300 | |a 157 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Advances in numerical mathematics | |
| 502 | |a Zugl.: Berlin, Freie Univ., Habil.-Schr., 1995 | ||
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Record in the Search Index
| _version_ | 1804125703013138432 |
|---|---|
| adam_text | Contents
Introduction 0
1 Nonlinear Variational Problems 12
1.1 Free and Moving Boundary Problems 12
1.1.1 Deformation of a Membrane with a Rigid Obstacle 13
1.1.2 A Semi Discrete Stefan Problem 15
1.1.3 The Semi Discrete Porous Medium Equation 19
1.2 Convex Minimization 22
1.2.1 The Continuous Problem 22
1.2.2 Variational Inequalities 26
1.2.3 Subdifferentials 32
1.3 Finite Element Discretization 36
1.3.1 The Discrete Problem 36
1.3.2 Convergence Results 38
2 Relaxation Methods 44
2.1 Basic Convergence Results 45
2.1.1 GauB Seidel Relaxation 45
2.1.2 Extended Relaxation Methods 51
2.2 Monotone Approximations 55
2.3 Asymptotic Properties: The Linear Reduced Problem 59
6 Contents
3 Monotone Multigrid Methods 65
3.1 Standard Monotone Multigrid Methods 66
3.1.1 The Multilevel Nodal Basis 66
3.1.2 Quasioptimal Approximations 69
3.1.3 Quasioptimal Restrictions 74
3.1.4 A Standard Multigrid V Cycle 77
3.2 Truncated Monotone Multigrid Methods 79
3.2.1 Truncation of the Multilevel Nodal Basis 79
3.2.2 Quasioptimal Approximations and Restrictions 81
3.2.3 A Truncated Multigrid V Cycle 82
3.3 Asymptotic Convergence Rates 83
3.3.1 A Modified Hierarchical Splitting 83
3.3.2 Final Convergence Results for the Standard Version 87
3.3.3 Final Convergence Results for the Truncated Version 91
4 A Posteriori Error Estimates and Adaptive Refinement 93
4.1 A Posteriori Estimates of the Approximation Error 94
4.1.1 A Discrete Defect Problem 95
4.1.2 An Error Estimate Based on Preconditioning 98
4.1.3 An Error Estimate Based on Nonlinear Iteration 103
4.2 A Stopping Criterion for the Adaptive Algorithm 108
4.3 Error Indicators and Local Refinement 108
4.4 A Stopping Criterion for the Iterative Solver 110
Contents 7
5 Numerical Results 113
5.1 Deformation of a Membrane with a Rigid Obstacle 113
5.1.1 The Adaptive Multilevel Method 114
5.1.2 The Monotone Multigrid Methods 116
5.1.3 The A Posteriori Error Estimates 118
5.2 A Strongly Reverse Biased p n Junction 120
5.2.1 The Adaptive Multilevel Method 123
5.2.2 The Monotone Multigrid Methods 124
5.2.3 The A Posteriori Error Estimates 126
5.3 Continuous Casting 127
5.3.1 The Adaptive Multilevel Method 131
5.3.2 The Monotone Multigrid Methods 135
5.3.3 The A Posteriori Error Estimates 137
5.4 The Porous Medium Equation 138
5.4.1 The Adaptive Multilevel Method 140
5.4.2 The Monotone Multigrid Methods 143
5.4.3 The A Posteriori Error Estimates 144
Notation 156
Index 158
|
| any_adam_object | 1 |
| author | Kornhuber, Ralf |
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| dewey-search | 515.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| isbn | 3519027224 |
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| spelling | Kornhuber, Ralf Verfasser aut Adaptive monotone multigrid methods for nonlinear variational problems von Ralf Kornhuber 1. Aufl. Stuttgart Teubner 1997 157 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in numerical mathematics Zugl.: Berlin, Freie Univ., Habil.-Schr., 1995 Multigrid methods (Numerical analysis) Variational inequalities (Mathematics) Nichtlineares Variationsproblem (DE-588)4234622-8 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Gitter-Verfahren gnd rswk-swf Nichtlineares Variationsproblem (DE-588)4234622-8 s Gitter-Verfahren f DE-604 Mehrgitterverfahren (DE-588)4038376-3 s Adaptives Verfahren (DE-588)4310560-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kornhuber, Ralf Adaptive monotone multigrid methods for nonlinear variational problems Multigrid methods (Numerical analysis) Variational inequalities (Mathematics) Nichtlineares Variationsproblem (DE-588)4234622-8 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Adaptives Verfahren (DE-588)4310560-9 gnd |
| subject_GND | (DE-588)4234622-8 (DE-588)4038376-3 (DE-588)4310560-9 (DE-588)4113937-9 |
| title | Adaptive monotone multigrid methods for nonlinear variational problems |
| title_auth | Adaptive monotone multigrid methods for nonlinear variational problems |
| title_exact_search | Adaptive monotone multigrid methods for nonlinear variational problems |
| title_full | Adaptive monotone multigrid methods for nonlinear variational problems von Ralf Kornhuber |
| title_fullStr | Adaptive monotone multigrid methods for nonlinear variational problems von Ralf Kornhuber |
| title_full_unstemmed | Adaptive monotone multigrid methods for nonlinear variational problems von Ralf Kornhuber |
| title_short | Adaptive monotone multigrid methods for nonlinear variational problems |
| title_sort | adaptive monotone multigrid methods for nonlinear variational problems |
| topic | Multigrid methods (Numerical analysis) Variational inequalities (Mathematics) Nichtlineares Variationsproblem (DE-588)4234622-8 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Adaptives Verfahren (DE-588)4310560-9 gnd |
| topic_facet | Multigrid methods (Numerical analysis) Variational inequalities (Mathematics) Nichtlineares Variationsproblem Mehrgitterverfahren Adaptives Verfahren Hochschulschrift Gitter-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kornhuberralf adaptivemonotonemultigridmethodsfornonlinearvariationalproblems |