Hierarchic models of elliptic boundary value problems on thin domains: a-posteriori error estimation and fourier analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
1995
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Stuttgart, Univ., Habil.-Schr., 1995 |
| Beschreibung: | 154 S. |
Internformat
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| 100 | 1 | |a Schwab, Christoph |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hierarchic models of elliptic boundary value problems on thin domains |b a-posteriori error estimation and fourier analysis |c Christoph Schwab |
| 264 | 1 | |c 1995 | |
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| 500 | |a Stuttgart, Univ., Habil.-Schr., 1995 | ||
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Datensatz im Suchindex
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| adam_text |
1
CONTENTS
1 INTRODUCTION 1
1.1 MOTIVATION AND GOALS OF THIS WORK. 1
1.2 OUTLINE AND RESULTS. 5
1.3 ACKNOWLEDGEMENT. 7
2 POISSON PROBLEM IN A THIN PLATE 8
2.1 NOTATION AND PROBLEM FORMULATION. 8
2.2 ASYMPTOTIC STRUCTURE OF THE SOLUTION. 10
2.2.1 A SEQUENCE OF DIRECTOR FUNCTIONS. 10
2.2.2 ASYMPTOTIC EXPANSION OF
U
. 11
2.3 A PRIORI ESTIMATES FOR THE BOUNDARY LAYERS. 14
2.3.1 AN ABSTRACT STABILITY ESTIMATE. 14
2.3.2 ESTIMATES FOR THE BOUNDARY LAYERS. 17
2.4 HIERARCHIC MODELS.20
2.5 A-PRIORI ESTIMATES OF THE MODELLING ERROR.24
2.5.1 COMPATIBLE DATA. 25
2.5.2 BOUNDARY LAYER RESOLUTION.-.25
2.6 A-POSTERIORI ESTIMATION OF THE MODELLING ERROR. 28
2.6.1 REPRESENTATION OF THE RESIDUAL. 28
2.6.2 DERIVATION OF THE MODELLING ERROR ESTIMATORS.30
2.6.3 LAMINATED MATERIALS.32
2.7 ASYMPTOTIC EXACTNESS OF THE ERROR ESTIMATOR. 34
2.8 SPECTRAL EXACTNESS OF THE ESTIMATOR. . 36
2.9 FUNDAMENTAL SOLUTION FOR THE HIERARCHIC MODELS .41
3 THE PLATE PROBLEM OF ELASTICITY I - ENERGY METHODS 44
3.1 PROBLEM FORMULATION.46
3.1.1 BASIC EQUATIONS.46
3.1.2 BOUNDARY CONDITIONS ON T. 48
3.1.3 PRINDAL VARIATIONAL FORMULATION. EXISTENCE. 50
3.1.4 DECOMPOSITION INTO MEMBRANE- AND BENDING PROBLEM.52
3.2 PLATE MODELS. 53
3.2.1 HIERARCHIC PLATE MODELS.53
3.2.2 REISSNER-MINDLIN MODEL .58
3.2.3 KIRCHHOFF MODEL.60
3.3 A-POSTERIORI MODELLING ERROR ESTIMATION FOR HIERARCHIC PLATE
MODELS.61
3.3.1 VARIATIONAL CHARACTERIZATION OF THE MODELLING ERROR.62
3.3.2 A-POSTERIORI ESTIMATION OF THE MODELLING ERROR -1. 65
3.3.3 ANALYSIS AND COMPUTATION OF THE CONSTANTS A
{{M)
. 69
3.3.4 A-POSTERIORI ESTIMATION OF THE MODELLING ERROR - II . . J.73
3.3.5 ASYMPTOTIC EXACTNESS OF THE ESTIMATOR.'.79
3.4 IMPLEMENTATION ASPECTS OF HIERARCHIC MODELS.82
3.4.1 PERFORMANCE OF THE MODELLING ERROR ESTIMATORS.83
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/946681651
2
O
R A 4 2 COMPUTATION OF ENGINEERING QUANTITIES.85
5
^'P10STEARLRI FDELLING ERROR ESTIMATION FOR THE REISSNER-MINDLIN MODEL
. 88
FT'1
YY
D AND DUAL FORMULATIONS OF THE PLATE PROBLEM.89
8.5.2 THEOREM OF PRAGER AND SYNGE . 91
3.5.3 REISSNER'S DERIVATION OF THE RM-MODEL.91
3.5.4 A-POSTERIORI MODELLING ERROR ESTIMATION.94
3.6 A-POSTERIORI MODELLING ERROR ESTIMATION FOR THE KIREHHOFF-LOVE-MODEL
. 96
4.2
4.3
4.4
4.5
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
THE PLATE PROBLEM OF ELASTICITY
II
- FOURIER METHODS
4.1 THE PLATE PROBLEM AND HIERARCHIC MODELS ON THE ELASTIC LAYER
FOURIER SOLUTIONS OF THE PLATE PROBLEM.
4.2.1 FOURIER TRANSFORMATION OF THE BOUNDARY VALUE PROBLEM
DECOMPOSITION INTO A TORSION- AND FLEXURE PART
INVERTIBILITY OF THE OPERATOR PENCIL LB(F) . . .
ANALYTIC CONTINUATION OF THE MULTIPLIER
DECOMPOSITION OF THE MULTIPLIER .
EXISTENCE AND A-PRIORI ESTIMATES .
FOURIER SOLUTIONS OF THE N-MODELS.
4.3.1 STRUCTURE OF THE MULTIPLIERS.
4.3.2 ANALYTIC CONTINUATION OF THE MULTIPLIERS
4.3.3 DECOMPOSITION OF THE MULTIPLIERS .
ASYMPTOTIC EXPANSION OF THE THREE-DIMENSIONAL SOLUTION
4.4.1 ASYMPTOTIC EXPANSION OF THE MULTIPLIERS ABOUT = 0
4.4.2 FORMAL ASYMPTOTICS OF THE THREE-DIMENSIONAL SOLUTION
4.4.3 ASYMPTOTIC ERROR ESTIMATES.
SAINT-VENANT PRINCIPLES AND APPLICATIONS.
4.5.1 EXPONENTIAL A-PRIORI ESTIMATES.
4.5.2 ANALYSIS OF THE SAINT-VENANT PROBLEM FOR PLATES .
4.5.3 INTERIOR A-PRIORI ESTIMATES OF THE ASYMPTOTIC EXPANSION
4.5.4 BOUNDARY LAYER RESOLUTION.
ERROR
101
. 102
. 103
. 103
. 105
. 107
. 109
. 110
. 112
. 113
. 114
. 116
. 119
. 124
. 124
. 125
. 127
. 132
. 132
. 137
. 139
. 140
5 REFERENCES
142
6 APPENDICES
6.1 APPENDIX A
6.2 APPENDIX B
6.3 APPENDIX C
147
. 147
. 151
. 153 |
| any_adam_object | 1 |
| author | Schwab, Christoph |
| author_facet | Schwab, Christoph |
| author_role | aut |
| author_sort | Schwab, Christoph |
| author_variant | c s cs |
| building | Verbundindex |
| bvnumber | BV010662085 |
| classification_tum | MAT 355d |
| ctrlnum | (OCoLC)632435675 (DE-599)BVBBV010662085 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010662085 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-09T16:14:28Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007117003 |
| oclc_num | 632435675 |
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| owner | DE-91 DE-BY-TUM DE-83 |
| owner_facet | DE-91 DE-BY-TUM DE-83 |
| physical | 154 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
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| spelling | Schwab, Christoph Verfasser aut Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis Christoph Schwab 1995 154 S. txt rdacontent n rdamedia nc rdacarrier Stuttgart, Univ., Habil.-Schr., 1995 Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf A-posteriori-Abschätzung (DE-588)4346907-3 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Plattentheorie (DE-588)4174891-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Plattentheorie (DE-588)4174891-8 s Elliptisches Randwertproblem (DE-588)4193399-0 s Fourier-Transformation (DE-588)4018014-1 s A-posteriori-Abschätzung (DE-588)4346907-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007117003&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwab, Christoph Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis Elliptisches Randwertproblem (DE-588)4193399-0 gnd A-posteriori-Abschätzung (DE-588)4346907-3 gnd Fourier-Transformation (DE-588)4018014-1 gnd Plattentheorie (DE-588)4174891-8 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4346907-3 (DE-588)4018014-1 (DE-588)4174891-8 (DE-588)4113937-9 |
| title | Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis |
| title_auth | Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis |
| title_exact_search | Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis |
| title_full | Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis Christoph Schwab |
| title_fullStr | Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis Christoph Schwab |
| title_full_unstemmed | Hierarchic models of elliptic boundary value problems on thin domains a-posteriori error estimation and fourier analysis Christoph Schwab |
| title_short | Hierarchic models of elliptic boundary value problems on thin domains |
| title_sort | hierarchic models of elliptic boundary value problems on thin domains a posteriori error estimation and fourier analysis |
| title_sub | a-posteriori error estimation and fourier analysis |
| topic | Elliptisches Randwertproblem (DE-588)4193399-0 gnd A-posteriori-Abschätzung (DE-588)4346907-3 gnd Fourier-Transformation (DE-588)4018014-1 gnd Plattentheorie (DE-588)4174891-8 gnd |
| topic_facet | Elliptisches Randwertproblem A-posteriori-Abschätzung Fourier-Transformation Plattentheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007117003&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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