Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations:
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| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos-Verl.
2015
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 188 S. graph. Darst. 24 cm |
| ISBN: | 9783832540678 3832540679 |
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MARC
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| 100 | 1 | |a Lellek, Dominik |d 1986- |e Verfasser |0 (DE-588)1076590349 |4 aut | |
| 245 | 1 | 0 | |a Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations |c Dominik Lellek |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2015 | |
| 300 | |a XI, 188 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Zugl.: Marburg, Univ., Diss., 2015 | ||
| 650 | 0 | 7 | |a Adaptives Verfahren |0 (DE-588)4310560-9 |2 gnd |9 rswk-swf |
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| 653 | |a Philipps-Universität Marburg | ||
| 653 | |a Partielle Differentialgleichungen | ||
| 653 | |a Numerik | ||
| 653 | |a Adaptivität | ||
| 653 | |a Wavelets | ||
| 653 | |a Nichtlineare Approximation | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1809772262529695744 |
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CONTENTS
INTRODUCTION 1
1 SEMILINEAR ELLIPTIC EQUATIONS 11
1.1 DOMAINS AND FUNCTION SPACES 13
1.2 WEAK FORMULATION 16
1.3 EXAMPLES 19
1.4 THE STATIONARY NAVIER-STOKES EQUATION 21
2 WAVELET BASES AND FRAMES 25
2.1 RIESZ BASES AND FRAMES IN HILBERT SPACES 25
2.1.1 RIESZ BASES 26
2.1.2 HILBERT FRAMES 27
2.1.3 GELFAND FRAMES 28
2.2 WAVELET RIESZ BASES AND WAVELET FRAMES 29
2.2.1 CONSTRUCTION PRINCIPLES ON THE REAL LINE 30
2.2.2 CONSTRUCTION PRINCIPLES ON BOUNDED DOMAINS 32
2.2.3 SPLINE WAVELETS ON THE INTERVAL 36
2.2.4 FROM THE INTERVAL TO THE UNIT CUBE 38
2.2.5 WAVELET FRAMES 40
2.2.6 DIVERGENCE-FREE WAVELETS 45
2.3 DISCRETIZATION WITH WAVELET FRAMES 48
2.3.1 SEMILINEAR ELLIPTIC EQUATIONS 48
2.3.2 STATIONARY NAVIER-STOKES EQUATION 51
3 NONLINEAR WAVELET APPROXIMATION AND REGULARITY 53
3.1 BASICS OF APPROXIMATION THEORY 54
3.1.1 APPROXIMATION SPACES 54
3.1.2 BESOV SPACES AND THEIR INTERPOLATION 54
3.2 APPROXIMATION WITH WAVELET BASES 58
3.2.1 LINEAR APPROXIMATION WITH WAVELET BASES 58
3.2.2 NONLINEAR APPROXIMATION WITH WAVELET BASES 59
3.3 UNRESTRICTED NONLINEAR APPROXIMATION IN 61
3.3.1 ./V-TERM APPROXIMATION 62
3.3.2 A
F
-TERM APPROXIMATION AND WAVELET RIESZ BASES 63
3.3.3 A
R
-TERM APPROXIMATION AND WAVELET FRAMES 64
LX
HTTP://D-NB.INFO/107628213X
CONTENTS
3.4 TREE-STRUCTURED APPROXIMATION IN 2 66
3.4.1 TREES AND AGGREGATED TREES 67
3.4.2 TV-TERM TREE APPROXIMATION AND WAVELET RIESZ BASES 70
3.4.3 ,/V-TERM AGGREGATED TREE APPROXIMATION AND WAVELET FRAMES . . 71
3.4.4 AGGREGATED TREE APPROXIMATION AND ASYMPTOTIC OPTIMALITY . . 73
3.5 REGULARITY OF SOLUTIONS TO ELLIPTIC EQUATIONS 74
3.5.1 REGULARITY OF LINEAR ELLIPTIC EQUATIONS 74
3.5.2 REGULARITY OF NONLINEAR ELLIPTIC EQUATIONS 77
4 ADAPTIVE WAVELET SCHWARZ METHODS 81
4.1 BASIC PRINCIPLES 82
4.1.1 MULTIPLICATIVE SCHWARZ METHOD 82
4.1.2 ADDITIVE SCHWARZ METHOD 89
4.2 BUILDING BLOCKS 93
4.2.1 COARSENING METHODS 93
4.2.2 EVALUATION OF MATRIX-VECTOR PRODUCTS 96
4.2.3 EVALUATION OF NONLINEAR EXPRESSIONS 100
4.2.4 EVALUATION OF THE RIGHT-HAND SIDE 106
4.3 ADAPTIVE MULTIPLICATIVE WAVELET SCHWARZ METHOD 107
4.3.1 CONTROLLING REDUNDANCIES BY A PROJECTION STEP 107
4.3.2 THE ADAPTIVE METHOD AND ITS CONVERGENCE 110
4.3.3 SOLUTION OF THE LOCAL SUBPROBLEMS 112
4.3.4 OPTIMALITY OF THE ADAPTIVE METHOD 117
4.4 ADAPTIVE ADDITIVE WAVELET SCHWARZ METHOD 121
4.4.1 THE ADAPTIVE METHOD AND ITS CONVERGENCE 121
4.4.2 SOLUTION OF THE LOCAL SUBPROBLEMS 122
4.4.3 OPTIMALITY OF THE ADAPTIVE METHOD 123
5 NUMERICAL TESTS 125
5.1 THE PRACTICAL IMPLEMENTATION OF THE METHODS 125
5.2 NUMERICAL TESTS ON THE INTERVAL 126
5.3 NUMERICAL TESTS ON THE L-SHAPED DOMAIN 135
5.4 SOME MODIFICATIONS AND IMPROVEMENTS 141
6 ADAPTIVE WAVELET SCHWARZ METHODS FOR THE NAVIER-STOKES EQUATION 143
6.1 THE BASIC PRINCIPLES OF THE ALGORITHM 144
6.2 AN ALTERNATIVE PROJECTION STRATEGY 146
6.3 THE ADAPTIVE WAVELET METHOD 153
6.4 ON THE NUMERICAL SOLUTION OF THE SUBPROBLEMS 156
7 ADAPTIVE NEWTON-SCHWARZ METHOD 159
7.1 THE BASIC APPROACH 160
7.2 THE ADAPTIVE NEWTON-SCHWARZ ALGORITHM 164
X
CONTENTS
7.3 REMARKS ON THE SOLUTION OF THE SUBPROBLEMS 167
7.4 NUMERICAL TESTS 169
CONCLUSION 173
LIST OF FIGURES 177
BIBLIOGRAPHY 179
XI |
| any_adam_object | 1 |
| author | Lellek, Dominik 1986- |
| author_GND | (DE-588)1076590349 |
| author_facet | Lellek, Dominik 1986- |
| author_role | aut |
| author_sort | Lellek, Dominik 1986- |
| author_variant | d l dl |
| building | Verbundindex |
| bvnumber | BV042981155 |
| classification_rvk | SK 920 |
| ctrlnum | (OCoLC)921524511 (DE-599)DNB107628213X |
| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| isbn | 9783832540678 3832540679 |
| language | English |
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| spelling | Lellek, Dominik 1986- Verfasser (DE-588)1076590349 aut Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations Dominik Lellek Berlin Logos-Verl. 2015 XI, 188 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Marburg, Univ., Diss., 2015 Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Gebietszerlegungsmethode (DE-588)4309232-9 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Philipps-Universität Marburg Partielle Differentialgleichungen Numerik Adaptivität Wavelets Nichtlineare Approximation (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s Gebietszerlegungsmethode (DE-588)4309232-9 s Wavelet (DE-588)4215427-3 s Adaptives Verfahren (DE-588)4310560-9 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=84ae4922c68c46509879251b07edff48&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028406643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lellek, Dominik 1986- Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations Adaptives Verfahren (DE-588)4310560-9 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4310560-9 (DE-588)4310554-3 (DE-588)4309232-9 (DE-588)4215427-3 (DE-588)4113937-9 |
| title | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations |
| title_auth | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations |
| title_exact_search | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations |
| title_full | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations Dominik Lellek |
| title_fullStr | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations Dominik Lellek |
| title_full_unstemmed | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations Dominik Lellek |
| title_short | Adaptive wavelet Schwarz methods for nonlinear elliptic partial differential equations |
| title_sort | adaptive wavelet schwarz methods for nonlinear elliptic partial differential equations |
| topic | Adaptives Verfahren (DE-588)4310560-9 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Adaptives Verfahren Nichtlineare elliptische Differentialgleichung Gebietszerlegungsmethode Wavelet Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=84ae4922c68c46509879251b07edff48&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028406643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lellekdominik adaptivewaveletschwarzmethodsfornonlinearellipticpartialdifferentialequations |