Optimal control of elliptic variational inequalities: numerical methods and point tracking objectives
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Uelvesbüll
<<Der>> Andere Verl.
2015
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 204 S. graph. Darst. |
| ISBN: | 9783862475186 |
Internformat
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| 245 | 1 | 0 | |a Optimal control of elliptic variational inequalities |b numerical methods and point tracking objectives |c by Caroline Babette Löbhard |
| 264 | 1 | |a Uelvesbüll |b <<Der>> Andere Verl. |c 2015 | |
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| 502 | |a Zugl.: Berlin, Humboldt-Univ., Diss., 2014 | ||
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| 650 | 0 | 7 | |a Elliptische Variationsungleichung |0 (DE-588)4479963-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804153290228760576 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
2 MATHEMATICAL PRELIMINARIES 7
2.1 NOTATION AND TOOLS FROM FUNCTIONAL ANALYSIS 7
2.2 NOTATION AND TOOLS FROM OPTIMIZATION 15
2.3 REVIEW ON ELLIPTIC VARIATIONAL INEQUALITIES 20
2.4 REVIEW ON THE OPTIMAL CONTROL OF VARIATIONAL INEQUALITIES . . 30
2.5 NOTATION AND TOOLS FROM NUMERICAL ANALYSIS 36
I TRACKING TYPE OPTIMA) CONTROL OF ELLIPTIC VARIATIONAL INEQUAL
ITIES 41
3 AN ELASTIC MODE PENALTY ALGORITHM 45
3.1 SOLVABILITY AND CONSISTENCY OF THE PENALIZATION SCHEME .... 45
3.2 LIMITING ANALYSIS OF FIRST ORDER STATIONARITY CONDITIONS ... 50
3.3 REMARKS ON EXACTNESS OF THE PENALTY SCHEME 58
3.4 RESULTING SOLUTION METHOD 63
4 AN ADAPTIVE METHOD FOR THE TRACKING TYPE FUNCTIONAL CASE 67
4.1 A PRIORI ESTIMATES FOR SOLUTIONS OF THE OPTIMALITY SYSTEM ... 67
4.2 ABSTRACT DISCRETE STATIONARITY CONDITIONS 73
4.3 ABSTRACT ERROR REPRESENTATION FORMULA 78
4.4 PRIMAL-DUAL-WEIGHTED A POSTERIORI ESTIMATOR 85
5 NUMERICAL TESTS 91
5.1 SOME DETAILS ON THE IMPLEMENTATION 91
5.2 COLLECTION OF TEST EXAMPLES 96
5.3 NUMERICAL RESULTS FOR THE ADAPTIVE METHOD 99
5.4 NUMERICAL RESULTS FOR THE ELASTIC MODE ALGORITHM 104
HTTP://D-NB.INFO/1072705729
VIII
C. L&BHARD: OPTIMAL CONTROL OF ELLIPTIC VARIATIONAL INEQUALITIES
II POINT-TRACKING OPTIMAL CONTROL OF ELLIPTIC VARIATIONAL INEQUAL
ITIES 111
6 OPTIMAL CONTROL OF VARIATIONAL INEQUALITIES WITH POINT-TRACKING 115
6.1 PROBLEM STATEMENT AND SOLVABILITY 115
6.2 PENALTY SCHEME 124
6.3 DERIVATION OF STATIONARITY CONDITIONS 129
7 AN ELASTIC MODE PENALTY METHOD FOR POINT TRACKING CONTROL OF VARI
ATIONAL INEQUALITIES 139
7.1 MODEL PROBLEM, PENALTY SCHEME: SOLVABILITY AND CONSISTENCY 139
7.2 LIMITING STATIONARITY CONDITIONS 146
7.3 RESULTING SOLUTION METHOD 157
8 AN ADAPTIVE METHOD FOR THE POINT TRACKING CASE 159
8.1 ABSTRACT ERROR REPRESENTATION FORMULA 159
8.2 DETAILED FINITE ELEMENT DISCRETIZATION 164
8.3 PRIMAL-DUAL WEIGHTED A POSTERIORI ESTIMATOR 166
9 NUMERICAL TESTS 169
9.1 COLLECTION OF TEST EXAMPLES 169
9.2 NUMERICAL RESULTS FOR THE ADAPTIVE METHOD 173
9.3 SOME DETAILS ON THE IMPLEMENTATION OF THE PENALTY METHOD . 175
9.4 NUMERICAL RESULTS FOR THE ELASTIC MODE ALGORITHM 177
A TABULATED NUMERICAL RESULTS 183
BIBLIOGRAPHY
191
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| any_adam_object | 1 |
| author | Löbhard, Caroline Babette |
| author_GND | (DE-588)1077837909 |
| author_facet | Löbhard, Caroline Babette |
| author_role | aut |
| author_sort | Löbhard, Caroline Babette |
| author_variant | c b l cb cbl |
| building | Verbundindex |
| bvnumber | BV042530881 |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)915652712 (DE-599)BVBBV042530881 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV042530881 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:24:15Z |
| institution | BVB |
| isbn | 9783862475186 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027965109 |
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| physical | VIII, 204 S. graph. Darst. |
| publishDate | 2015 |
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| publisher | <<Der>> Andere Verl. |
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| spelling | Löbhard, Caroline Babette Verfasser (DE-588)1077837909 aut Optimal control of elliptic variational inequalities numerical methods and point tracking objectives by Caroline Babette Löbhard Uelvesbüll <<Der>> Andere Verl. 2015 VIII, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zugl.: Berlin, Humboldt-Univ., Diss., 2014 Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Elliptische Variationsungleichung (DE-588)4479963-9 gnd rswk-swf Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Optimale Kontrolle (DE-588)4121428-6 s Elliptische Variationsungleichung (DE-588)4479963-9 s Finite-Elemente-Methode (DE-588)4017233-8 s Adaptives Verfahren (DE-588)4310560-9 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027965109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Löbhard, Caroline Babette Optimal control of elliptic variational inequalities numerical methods and point tracking objectives Optimale Kontrolle (DE-588)4121428-6 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Elliptische Variationsungleichung (DE-588)4479963-9 gnd Adaptives Verfahren (DE-588)4310560-9 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4017233-8 (DE-588)4479963-9 (DE-588)4310560-9 (DE-588)4113937-9 |
| title | Optimal control of elliptic variational inequalities numerical methods and point tracking objectives |
| title_auth | Optimal control of elliptic variational inequalities numerical methods and point tracking objectives |
| title_exact_search | Optimal control of elliptic variational inequalities numerical methods and point tracking objectives |
| title_full | Optimal control of elliptic variational inequalities numerical methods and point tracking objectives by Caroline Babette Löbhard |
| title_fullStr | Optimal control of elliptic variational inequalities numerical methods and point tracking objectives by Caroline Babette Löbhard |
| title_full_unstemmed | Optimal control of elliptic variational inequalities numerical methods and point tracking objectives by Caroline Babette Löbhard |
| title_short | Optimal control of elliptic variational inequalities |
| title_sort | optimal control of elliptic variational inequalities numerical methods and point tracking objectives |
| title_sub | numerical methods and point tracking objectives |
| topic | Optimale Kontrolle (DE-588)4121428-6 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Elliptische Variationsungleichung (DE-588)4479963-9 gnd Adaptives Verfahren (DE-588)4310560-9 gnd |
| topic_facet | Optimale Kontrolle Finite-Elemente-Methode Elliptische Variationsungleichung Adaptives Verfahren Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027965109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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