Wavelet methods - elliptic boundary value problems and control problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart [u.a.]
Teubner
2001
|
| Edition: | 1. Aufl. |
| Series: | Advances in numerical mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 140 S. Ill., graph. Darst. |
| ISBN: | 3519003279 |
Staff View
MARC
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| 245 | 1 | 0 | |a Wavelet methods - elliptic boundary value problems and control problems |c von Angela Kunoth |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Stuttgart [u.a.] |b Teubner |c 2001 | |
| 300 | |a 140 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Advances in numerical mathematics | |
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| 650 | 4 | |a Differential equations, Elliptic |x Numerical solutions | |
| 650 | 4 | |a Wavelets (Mathematics) | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
2 The General Concept 6
3 Wavelets 13
3.1 Preliminaries 13
3.2 Multiscale Decomposition of Function Spaces — Uniform Refinements . . 14
3.2.1 Multiresolution of Li 14
3.2.2 Multiresolution of Sobolev Spaces and Norm Equivalences .... 21
3.2.3 Reverse Cauchy Schwarz Inequalities 23
3.2.4 Preconditioning 24
3.2.5 An Example of Biorthogonal Wavelets on M 25
3.3 Wavelets on an Interval 27
3.4 Wavelets on Manifolds 29
3.4.1 Domain Decomposition Approaches 29
3.4.2 The Cartesian Product Approach 31
3.5 Multiscale Decomposition of Function Spaces — Non Uniform Refinements 33
4 Elliptic Boundary Value Problems 34
4.1 General Saddle Point Problems 34
4.1.1 The Continuous Abstract Saddle Point Problem 34
4.1.2 Discretization and Preconditioning 36
4.1.3 The Discrete Finite Problem 37
4.1.4 Error Estimates and Iterative Solution 38
4.2 Elliptic Boundary Value Problems as Saddle Point Problems 39
4.2.1 The Fictitious Domain—Lagrange Multiplier Approach 40
4.2.2 Trace Theorems 44
4.2.3 Conditions Ensuring Stability of the Discretizations: General Re¬
marks 46
4.2.4 Conditions Ensuring Stability of the Discretizations: The LBB
Condition 47
4.3 Numerical Studies 55
5 Least Squares Problems 69
5.1 Introduction 69
5.2 General Setting 71
5.3 Least Squares Formulation of General Saddle Point Problems 73
5.4 Wavelet Representation of Least Squares Systems 76
5.5 Truncation 82
5.6 Preconditioning and Computational Work 87
5.7 Numerical Experiments 88
6 Control Problems 95
6.1 Introduction 95
6.2 The Continuous Case: Two Coupled Saddle Point Problems 99
6.3 Discretization and Preconditioning 106
6.4 The Discrete Finite Dimensional Problem 109
6.5 Iterative Methods for WSPP(A, A) 110
6.6 Alternative Iterative Methods for the Coupled System Ill
6.6.1 Semi Iterative Methods 112
6.6.2 Block Kaczmarz Iteration 113
6.6.3 A Fully Iterative Method for Coupled Saddle Point Problems ... 114
6.6.4 Computational Work for Algorithm OutIt 121
6.6.5 A Numerical Example 125
6.7 Outlook into Nonlinear Problems and Adaptive Strategies 128
References 129
Index 139
|
| any_adam_object | 1 |
| author | Kunoth, Angela 1963- |
| author_GND | (DE-588)122898125 |
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| ctrlnum | (OCoLC)248717406 (DE-599)BVBBV013653223 |
| dewey-full | 515/.2433 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| id | DE-604.BV013653223 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:49:39Z |
| institution | BVB |
| isbn | 3519003279 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009328780 |
| oclc_num | 248717406 |
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| owner | DE-29T DE-703 DE-355 DE-BY-UBR DE-92 DE-706 |
| owner_facet | DE-29T DE-703 DE-355 DE-BY-UBR DE-92 DE-706 |
| physical | 140 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Teubner |
| record_format | marc |
| series2 | Advances in numerical mathematics |
| spelling | Kunoth, Angela 1963- Verfasser (DE-588)122898125 aut Wavelet methods - elliptic boundary value problems and control problems von Angela Kunoth 1. Aufl. Stuttgart [u.a.] Teubner 2001 140 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in numerical mathematics Ondelettes Équations différentielles elliptiques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Wavelets (Mathematics) Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Regelungstheorie (DE-588)4122327-5 gnd rswk-swf Wavelet (DE-588)4215427-3 s Elliptisches Randwertproblem (DE-588)4193399-0 s Regelungstheorie (DE-588)4122327-5 s DE-604 Kontrolltheorie (DE-588)4032317-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kunoth, Angela 1963- Wavelet methods - elliptic boundary value problems and control problems Ondelettes Équations différentielles elliptiques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Wavelets (Mathematics) Elliptisches Randwertproblem (DE-588)4193399-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd Wavelet (DE-588)4215427-3 gnd Regelungstheorie (DE-588)4122327-5 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4032317-1 (DE-588)4215427-3 (DE-588)4122327-5 |
| title | Wavelet methods - elliptic boundary value problems and control problems |
| title_auth | Wavelet methods - elliptic boundary value problems and control problems |
| title_exact_search | Wavelet methods - elliptic boundary value problems and control problems |
| title_full | Wavelet methods - elliptic boundary value problems and control problems von Angela Kunoth |
| title_fullStr | Wavelet methods - elliptic boundary value problems and control problems von Angela Kunoth |
| title_full_unstemmed | Wavelet methods - elliptic boundary value problems and control problems von Angela Kunoth |
| title_short | Wavelet methods - elliptic boundary value problems and control problems |
| title_sort | wavelet methods elliptic boundary value problems and control problems |
| topic | Ondelettes Équations différentielles elliptiques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Wavelets (Mathematics) Elliptisches Randwertproblem (DE-588)4193399-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd Wavelet (DE-588)4215427-3 gnd Regelungstheorie (DE-588)4122327-5 gnd |
| topic_facet | Ondelettes Équations différentielles elliptiques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Wavelets (Mathematics) Elliptisches Randwertproblem Kontrolltheorie Wavelet Regelungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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