Finite element error analysis for PDE-constrained optimal control problems: the control constrained case under reduced regularity
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2010
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20100716-977779-1-3 Inhaltsverzeichnis |
| Physical Description: | VIII, 165 S. graph. Darst. |
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| 100 | 1 | |a Sirch, Dieter Sebastian |d 1981- |e Verfasser |0 (DE-588)141994134 |4 aut | |
| 245 | 1 | 0 | |a Finite element error analysis for PDE-constrained optimal control problems |b the control constrained case under reduced regularity |c Dieter Sebastian Sirch |
| 264 | 1 | |c 2010 | |
| 300 | |a VIII, 165 S. |b graph. Darst. | ||
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| 502 | |a München, Techn. Univ., Diss., 2010 | ||
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Record in the Search Index
| _version_ | 1804143216481533952 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
1.1 MOTIVATION 1
1.2 STATE EQUATION 2
1.3 OPTIMAL CONTROL PROBLEMS 4
1.4 OUTLINE 5
PRELIMINARIES 9
2.1 BASIC FACTS FROM FUNCTIONAL ANALYSIS 9
2.2 FUNCTION SPACES 11
2.3 GRADED TRIANGULATIONS 16
2.3.1 TWO-DIMENSIONAL DOMAIN 16
2.3.2 THREE-DIMENSIONAL DOMAIN 17
INTERPOLATION OF NONSMOOTH FUNCTIONS 19
3.1 SUITABLE INTERPOLATION OPERATORS 19
3.2 TENSOR PRODUCT MESHES 20
3.3 QUASI-INTERPOLATION OPERATORS 22
3.4 LOCAL ESTIMATES IN CLASSICAL SOBOLEV SPACES 24
3.5 LOCAL ESTIMATES IN WEIGHTED SOBOLEV SPACES 30
3.6 EXTENSION TO MORE GENERAL MESHES 33
FINITE ELEMENT ERROR ESTIMATES FOR BOUNDARY VALUE PROBLEMS 35 4.1 SCALAR
ELLIPTIC EQUATIONS IN POLYGONAL DOMAINS 35
4.1.1 REGULARITY 36
4.1.2 FINITE ELEMENT ERROR ESTIMATES 37
4.2 SCALAR ELLIPTIC EQUATIONS IN PRISMATIC DOMAINS 52
4.2.1 REGULARITY 53
4.2.2 FINITE ELEMENT ERROR ESTIMATES 58
4.3 SCALAR ELLIPTIC EQUATIONS WITH NONSMOOTH COEFFICIENTS 63
4.3.1 REGULARITY 64
4.3.2 FINITE ELEMENT ERROR ESTIMATES 65
VU
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005910162
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
4.4 STOKES EQUATIONS IN NONSMOOTH DOMAINS 65
4.4.1 GENERAL SITUATION 66
4.4.2 STOKES EQUATIONS IN POLYGONAL DOMAINS 71
4.4.3 STOKES EQUATIONS IN PRISMATIC DOMAINS 79
5 ERROR ESTIMATES FOR PDE-CONSTRAINED OPTIMAL CONTROL PROBLEMS 83 5.1
ANALYSIS FOR GENERAL LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS 83 5.1.1
EXISTENCE AND UNIQUENESS OF A SOLUTION 84
5.1.2 DISCRETIZATION CONCEPTS 84
5.2 SCALAR ELLIPTIC STATE EQUATION 93
5.2.1 POLYGONAL DOMAIN 94
5.2.2 PRISMATIC DOMAIN 108
5.2.3 NONSMOOTH COEFFICIENTS 121
5.3 STOKES EQUATIONS AS STATE EQUATION 127
5.3.1 PRISMATIC DOMAIN 129
5.3.2 POLYGONAL DOMAIN 138
6 CONCLUSION AND OUTLOOK 143
A NOTATION 145
B THE SOFTWARE PACKAGE OPTPDE 147
B.I STRUCTURE OF OPTPDE 147
B.2 OPTIMIZATION PART 147
B.3 FINITE ELEMENT LIBRARY 150
BIBLIOGRAPHY 153
|
| any_adam_object | 1 |
| author | Sirch, Dieter Sebastian 1981- |
| author_GND | (DE-588)141994134 |
| author_facet | Sirch, Dieter Sebastian 1981- |
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| author_sort | Sirch, Dieter Sebastian 1981- |
| author_variant | d s s ds dss |
| building | Verbundindex |
| bvnumber | BV036610926 |
| classification_tum | MAT 674d MAT 661d MAT 496d MAT 355d |
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| dewey-full | 515.642 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.642 |
| dewey-search | 515.642 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T22:44:08Z |
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| language | English |
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| physical | VIII, 165 S. graph. Darst. |
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| spelling | Sirch, Dieter Sebastian 1981- Verfasser (DE-588)141994134 aut Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity Dieter Sebastian Sirch 2010 VIII, 165 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2010 Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf A-priori-Abschätzung (DE-588)4304925-4 gnd rswk-swf Fehleranalyse (DE-588)4016608-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Optimale Kontrolle (DE-588)4121428-6 s Finite-Elemente-Methode (DE-588)4017233-8 s A-priori-Abschätzung (DE-588)4304925-4 s Fehleranalyse (DE-588)4016608-9 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20100716-977779-1-3 https://mediatum.ub.tum.de/node?id=977779 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20100716-977779-1-3 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020531187&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sirch, Dieter Sebastian 1981- Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity Elliptische Differentialgleichung (DE-588)4014485-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd A-priori-Abschätzung (DE-588)4304925-4 gnd Fehleranalyse (DE-588)4016608-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4121428-6 (DE-588)4304925-4 (DE-588)4016608-9 (DE-588)4017233-8 (DE-588)4113937-9 |
| title | Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity |
| title_auth | Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity |
| title_exact_search | Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity |
| title_full | Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity Dieter Sebastian Sirch |
| title_fullStr | Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity Dieter Sebastian Sirch |
| title_full_unstemmed | Finite element error analysis for PDE-constrained optimal control problems the control constrained case under reduced regularity Dieter Sebastian Sirch |
| title_short | Finite element error analysis for PDE-constrained optimal control problems |
| title_sort | finite element error analysis for pde constrained optimal control problems the control constrained case under reduced regularity |
| title_sub | the control constrained case under reduced regularity |
| topic | Elliptische Differentialgleichung (DE-588)4014485-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd A-priori-Abschätzung (DE-588)4304925-4 gnd Fehleranalyse (DE-588)4016608-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Elliptische Differentialgleichung Optimale Kontrolle A-priori-Abschätzung Fehleranalyse Finite-Elemente-Methode Hochschulschrift |
| url | https://mediatum.ub.tum.de/node?id=977779 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20100716-977779-1-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020531187&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sirchdietersebastian finiteelementerroranalysisforpdeconstrainedoptimalcontrolproblemsthecontrolconstrainedcaseunderreducedregularity |