Hp-Finite elements for PDE-constrained optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Electronic eBook |
| Language: | English |
| Published: |
Würzburg
Würzburg University Press
2015
|
| Subjects: | |
| Online Access: | Volltext Inhaltsverzeichnis |
| Physical Description: | XIV, 174 Seiten Illustrationen, Diagramme |
| ISBN: | 9783958260245 |
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MARC
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| 100 | 1 | |a Wurst, Jan-Eric |e Verfasser |0 (DE-588)1042405573 |4 aut | |
| 245 | 1 | 0 | |a Hp-Finite elements for PDE-constrained optimization |c Jan-Eric Wurst |
| 264 | 1 | |a Würzburg |b Würzburg University Press |c 2015 | |
| 300 | |a XIV, 174 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 502 | |b Dissertation |c Julius-Maximilians-Universität Würzburg, Fakultät für Mathematik und Informatik |d 2015 | ||
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Record in the Search Index
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| adam_text | CONTENTS
PREFACE V*
LIST OF SYMBOLS AND ABBREVIATIONS XI
1 INTRODUCTION 1
1.1 THE FINITE ELEMENT M E TH O D
..................................................................... 1
1.2 APPLICATION TO CONTROL CONSTRAINED OPTIMIZATION PROBLEMS. ...... 4
1.3 SOLUTION TECHNIQUES AND THEIR MAIN I D E A S
.............................................
5
1.3.1 THE SEMI-SMOOTH NEWTON METHOD AND A-PRIORI DISCRETIZATIONS 5
1.3.2 THE INTERIOR POINT METHOD AND *-POSTERIORI DISCRETIZATIONS . . . 6
1.4 OUTLINE OF THE T H E
SIS.................................................................................
7
2 OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS 9
2.1 PRELIM
INARIES.............................................................................................
9
2.1.1 FUNCTIONAL
ANALYSIS........................................................................
10
2.1.2 THE
DOMAIN....................................................................................
11
2.1.3 FUNCTION SPACES
...........................................................................
12
2.2 THE MODEL PRNBLP
*
....................................................................................
17
2.2.1 SMOOTH NEUMANN PROBLEM
S......................................................... 18
2.2.2 TRANSMISSION
PROBLEMS..................................................................
19
2.3 SOLVABILITY AND OPTIMALITY
CONDITIONS...................................................... 20
3 REGULARITY RESULTS 23
3.1 CLASSICAL SOBOLEV-SLOBODE^ ................... 24
3.1.1 EXPANSIONS IN REGULAR AND SINGUL^^ ........ 24
3.1.2 LOWER BOUNDS FOR
EIGENVALUES...................................................... 33
3.2 ANALYTIC REGULARITY FAR FROM THE BOUNDARY AND INTERFACE ........ 37
3.3 ANALNIE REGULARITY FAR FROM SINGULAR P O IN
TS............................................. 39
3.3.1 PRELIMINARY ASSUMPTIONS AND R EM ARKS
.......................................
39
3.3.2 COVERING R E S U LTS
.....................................................................
..
. 41
3.3.3 LOCAL REGULARITY
...........................................................................
48
3.3.4 GLOBAL
REGULARITY...........................................................................
59
3.3.5 COMMENTS ON THE DERIVATION OF M LY TIC ITY
.................................
65
CONTENTS
4 THE HP-F N XE ELEMENT METHOD
4.1 GENERAL CONCEPTS .........
4.2 IMPLEMENTATIONAL REMARKS . . .
4.2.1 DESIGNING BASIS FUNCTIONS
4.2.2 THE ASSEMBLY PROCESS . .
4.3 ALGEBRAIC CONVERGENCE OF THE BOUNDARY CONCENTRATED FEM
4.3.1 ENERGY NORM E S TIM A TE S
..........................................
4.3.2 LEBESGUE NORM ESTIMATES AT THE BOUNDARY.....
4.4 EXPONENTIAL CONVERGENCE OF THE VERTEX CONCENTRATED FEM
5 NUMERICAL INVESTIGATIONS
5.1 VARIATIONAL DISCRETIZATION
...................................................
5.2 NEUMANN CONTROL P RO B LEM
S................................................
5.2.1 BOUNDARY CONCENTRATED FEM ............
5.2.2 VERTEX CONCENTRATED F E M
.......................................
5.2.3 BANG-BANG PROBLEM
S................................................
5.3 INTERFACE CONTROL
PROBLEMS...................................................
6 A PATH-FOLLOWING APPROACH
6.1 THE BARRIER PROBLEM AND CENTRAL PATH ...........
6.2 THE INTERIOR POINT M E TH O D
...................................................
6.2.1 AN ABSTRACT ALGORITHM IN FUNCTION
6.2.2 WELL*POSEDNESS
6.2.3 C
ONVERGENCE............................................................
6.3
DISCRETIZATION........................................................................
6.3.1 THE OPTIMALITY SYSTEM
.............................................
6.3.2 ESTIMATING SMOOTHNESS AND HP-ADAPTIVITY .....
6.3.3 A FULLY ADAPTIVE INTERIOR POINT
6.4 *-POSTERIORI ERROR
ESTIMATORS................................................
6.4.1 ERROR TO THE CENTRAL P A TH
..........................................
6.4.2 ERROR IN THE NEWTON S Y STEM
....................................
6.4.3 RESIDUAL BASED HP ERROR ESTIMATES .........
6.5 NUMERICAL E XAM
PLES............................................................
6.5.1 TESTING
ZIP-ADAPTIVITY................................................
6.5.2 TESTING ADAPTIVE PATH-FOLLOWING. ..........
7 CONCLUSION AND OUTLOOK
7.1 SEMI-SMOOTH NEWTON M E TH O D S
..........................................
7.2 PATH-FOLLOWING M ETH O D
S......................................................
7.3 NON-LINEAR STATE E Q U A TIO N
S................................................
7.4 STATE C
ONSTRAINTS..................................................................
7.5
MISCELLANEOUS........................................................................
BIBLIOGRAPHY
67
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9
0
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H
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VI
|
| any_adam_object | 1 |
| author | Wurst, Jan-Eric |
| author_GND | (DE-588)1042405573 |
| author_facet | Wurst, Jan-Eric |
| author_role | aut |
| author_sort | Wurst, Jan-Eric |
| author_variant | j e w jew |
| building | Verbundindex |
| bvnumber | BV043349218 |
| classification_rvk | SK 880 SK 910 |
| collection | ebook |
| ctrlnum | (OCoLC)955345863 (DE-599)BVBBV043349218 |
| dewey-full | 518.25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.25 |
| dewey-search | 518.25 |
| dewey-sort | 3518.25 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Electronic eBook |
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| id | DE-604.BV043349218 |
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| indexdate | 2024-07-10T07:23:40Z |
| institution | BVB |
| isbn | 9783958260245 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028768794 |
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| physical | XIV, 174 Seiten Illustrationen, Diagramme |
| psigel | ebook |
| publishDate | 2015 |
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| spelling | Wurst, Jan-Eric Verfasser (DE-588)1042405573 aut Hp-Finite elements for PDE-constrained optimization Jan-Eric Wurst Würzburg Würzburg University Press 2015 XIV, 174 Seiten Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Dissertation Julius-Maximilians-Universität Würzburg, Fakultät für Mathematik und Informatik 2015 Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s Optimale Kontrolle (DE-588)4121428-6 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:20-opus-115027 978-3-95826-025-2 https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-115027 Resolving-System kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028768794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wurst, Jan-Eric Hp-Finite elements for PDE-constrained optimization Optimale Kontrolle (DE-588)4121428-6 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4014485-9 (DE-588)4017233-8 (DE-588)4113937-9 |
| title | Hp-Finite elements for PDE-constrained optimization |
| title_auth | Hp-Finite elements for PDE-constrained optimization |
| title_exact_search | Hp-Finite elements for PDE-constrained optimization |
| title_full | Hp-Finite elements for PDE-constrained optimization Jan-Eric Wurst |
| title_fullStr | Hp-Finite elements for PDE-constrained optimization Jan-Eric Wurst |
| title_full_unstemmed | Hp-Finite elements for PDE-constrained optimization Jan-Eric Wurst |
| title_short | Hp-Finite elements for PDE-constrained optimization |
| title_sort | hp finite elements for pde constrained optimization |
| topic | Optimale Kontrolle (DE-588)4121428-6 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Optimale Kontrolle Elliptische Differentialgleichung Finite-Elemente-Methode Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-115027 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028768794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wurstjaneric hpfiniteelementsforpdeconstrainedoptimization |