Gespeichert in:
| Titel: | Numerical methods for nonlinear variational problems |
|---|---|
| Von: |
Roland Glowinski
|
| Person: |
Glowinski, Roland
1937-2022 Verfasser aut |
| Hauptverfasser: | |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Tokyo
Springer
1984
|
| Schriftenreihe: | Springer series in computational physics
|
| Schlagworte: | |
| Online-Zugang: | http://d-nb.info/840728042/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029758783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 435 - 453 |
| Beschreibung: | XIII, 493 Seiten 82 graph. Darst. 24 cm |
| ISBN: | 0387124349 3540124349 9783662126158 |
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Datensatz im Suchindex
| _version_ | 1819264690466848768 |
|---|---|
| adam_text | SOM
E PRELIMINAR
Y COMMENT
S XIV
CHAPTER
I
GENERALITIE
S ON ELLIPTI
C VARIATIONA
L INEQUALITIE
S AND O
N THEI
R
APPROXIMATIO
N 1
1. INTRODUCTIO
N 1
2. FUNCTIONA
L CONTEX
T 1
3. EXISTENC
E AN
D UNIQUENES
S RESULT
S FO
R EV
I O
F TH
E FIRS
T KIN
D 3
4
. EXISTENC
E AN
D UNIQUENES
S RESULT
S FO
R EV
I O
F TH
E SECON
D KIN
D 5
5. INTERNA
L APPROXIMATIO
N O
F EV
I O
F TH
E FIRS
T KIN
D 8
6. INTERNA
L APPROXIMATIO
N O
F EV
I O
F TH
E SECON
D KIN
D 12
7. PENALT
Y SOLUTIO
N O
F ELLIPTI
C VARIATIONA
L INEQUALITIE
S O
F TH
E FIRS
T KIN
D ..
. 15
8. REFERENCE
S 2
6
CHAPTER
II
APPLICATION OF THE FINITE ELEMENT METHOD TO THE APPROXIMATION OF
SOME SECOND-ORDER EVI 27
1. INTRODUCTIO
N 27
2. AN EXAMPLE OF EVI OF THE FIRST KIND
: THE OBSTACLE PROBLEM 27
3. A SECOND EXAMPLE OF EVI OF THE FIRST KIND
: THE ELASTO-PLASTIC TORSION
PROBLEM 41
4. A THIRD EXAMPLE OF EVI OF THE FIRST KIND
: A SIMPLIFIED SIGNORINI PROBLEM . 56
5. AN EXAMPLE OF EVI OF THE SECOND KIND
: A SIMPLIFIED FRICTION PROBLEM . . 68
6. A SECOND EXAMPLE OF EVI OF THE SECOND KIND
: THE FLOW OF A VISCOUS
PLASTIC FLUID IN A PIPE 78
7. ON SOME USEFUL FORMULA
E 96
CHAPTER
III
ON THE APPROXIMATION OF PARABOLIC VARIATIONAL INEQUALITIES 98
1. INTRODUCTION
: REFERENCES 98
2. FORMULATIO
N AND STATEMENT OF THE MAIN RESULTS 98
3. NUMERICAL SCHEMES FOR PARABOLIC LINEAR EQUATION
S 99
4. APPROXIMATION OF PVI OF THE FIRST KIND 101
HTTP://D-NB.INFO/840728042
5. APPROXIMATION OF PVI OF THE SECOND KIN
D 103
6. APPLICATION T
O A SPECIFIC EXAMPLE
: TIME-DEPENDENT FLOW OF A BINGHAM
FLUID IN A CYLINDRICAL PIPE 104
CHAPTER
IV
APPLICATION
S OF ELLIPTI
C VARIATIONA
L INEQUALIT
Y METHOD
S T
O THE SOLUTIO
N
O
F SOM
E NONLINEA
R ELLIPTI
C EQUATION
S 110
1. INTRODUCTION 110
2. THEORETICAL AND NUMERICAL ANALYSIS OF SOME MILDLY NONLINEAR ELLIPTIC
EQUATIONS 110
3. A SUBSONIC FLOW PROBLEM 134
CHAPTER
V
RELAXATIO
N METHOD
S AND APPLICATION
S 140
1. GENERALITIES 140
2. SOME BASIC RESULTS OF CONVEX ANALYSIS 140
3. RELAXATION METHODS FOR CONVEX FUNCTIONALS
: FINITE-DIMENSIONAL CASE . . 142
4. BLOCK RELAXATION METHODS 151
5. CONSTRAINED MINIMIZATION OF QUADRATI
C FUNCTIONALS IN HILBERT SPACES BY
UNDER AND OVER-RELAXATION METHODS
: APPLICATION 152
6. SOLUTION OF SYSTEMS OF NONLINEAR EQUATION
S BY RELAXATION METHODS . . . 163
CHAPTER
VI
DECOMPOSITION-COORDINATION METHOD
S BY AUGMENTED LAGRANGIAN
:
APPLICATIONS 166
1. INTRODUCTIO
N 166
2. PROPERTIES OF (P) AND OF THE SADDLE POINTS OF .? AND
R
168
3. DESCRIPTION OF THE ALGORITHMS 170
4. CONVERGENCE OF AL
G 1 171
5. CONVERGENCE OF AL
G 2 179
6. APPLICATIONS 183
7. GENERAL COMMENTS 194
CHAPTER
VII
LEAST-SQUARE
S SOLUTION OF NONLINEAR PROBLEMS
: APPLICATION T
O NONLINEA
R
PROBLEM
S IN FLUID DYNAMIC
S 195
1. INTRODUCTION
: SYNOPSI
S 195
2
. LEAST-SQUARE
S SOLUTIO
N OF FINITE-DIMENSIONA
L SYSTEM
S OF EQUATION
S ..
. 195
3
. LEAST-SQUARE
S SOLUTIO
N OF A NONLINEA
R DIRICHLE
T MODE
L PROBLE
M . . . .19
8
4
. TRANSONI
C FLO
W CALCULATION
S B
Y LEAST-SQUARE
S AN
D FINIT
E ELEMEN
T METHOD
S . 21
1
5. NUMERICA
L SOLUTIO
N O
F TH
E NAVIER-STOKE
S EQUATION
S FO
R INCOMPRESSIBL
E
VISCOU
S FLUID
S B
Y LEAST-SQUARE
S AN
D FINIT
E ELEMEN
T METHOD
S 24
4
6. FURTHE
R COMMENT
S O
N CHAPTE
R VI
I AN
D CONCLUSIO
N 318
APPENDIX
I
A BRIEF INTRODUCTION TO LINEAR VARIATIONAL PROBLEMS 321
1. INTRODUCTION 321
2. A FAMILY OF LINEAR VARIATIONAL PROBLEMS 321
3. INTERNAL APPROXIMATION OF PROBLEM (P) 326
4. APPLICATION TO THE SOLUTION OF ELLIPTIC PROBLEMS FOR PARTIAL
DIFFERENTIAL
OPERATORS 330
5. FURTHE
R COMMENTS
: CONCLUSION 397
APPENDIX
II
A
FINITE ELEMEN
T METHO
D WITH UPWINDIN
G FOR SECOND-ORDE
R PROBLEM
S
WITH LARG
E FIRST
- ORDE
R TERM
S 399
1. INTRODUCTION 399
2. THE MODEL PROBLEM 399
3. A CENTERED FINITE ELEMENT APPROXIMATIO
N 400
4. A FINITE ELEMENT APPROXIMATION WITH UPWINDING 400
5. ON THE SOLUTION OF THE LINEAR SYSTEM OBTAINED BY UPWINDING 404
6. NUMERICAL EXPERIMENTS 404
7. CONCLUDING COMMENTS 414
APPENDIX
III
SOME COMPLEMENTS ON THE NAVIER-STOKE
S EQUATIONS AND THEIR
NUMERICAL TREATMEN
T 415
1. INTRODUCTION 415
2. FINITE ELEMENT APPROXIMATION OF THE BOUNDARY CONDITIO
N U = GONFIFG^
0 415
3. SOME COMMENTS ON THE NUMERICAL TREATMEN
T OF THE NONLINEA
R TERM (U YY V)U 416
4. FURTHE
R COMMENTS ON THE BOUNDARY CONDITIONS 417
5. DECOMPOSITION PROPERTIES OF THE CONTINUOU
S AND DISCRETE STOKES PROBLEMS
OF SEC. 4. APPLICATION TO THEIR NUMERICAL SOLUTION 425
6. FURTHE
R COMMENTS 430
SOME ILLUSTRATIONS FROM AN INDUSTRIAL APPLICATION 431
BIBLIOGRAPHY 435
GLOSSARY OF SYMBOLS 455
AUTHOR INDEX 463
SUBJECT INDEX 467
|
| any_adam_object | 1 |
| author | Glowinski, Roland 1937-2022 |
| author_GND | (DE-588)120514737 |
| author_facet | Glowinski, Roland 1937-2022 |
| author_role | aut |
| author_sort | Glowinski, Roland 1937-2022 |
| author_variant | r g rg |
| building | Verbundindex |
| bvnumber | BV044356142 |
| ctrlnum | (DE-599)DNB840728042 |
| discipline | Physik Geographie |
| format | Book |
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| id | DE-604.BV044356142 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:00:47Z |
| institution | BVB |
| isbn | 0387124349 3540124349 9783662126158 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029758783 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | XIII, 493 Seiten 82 graph. Darst. 24 cm |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in computational physics |
| spellingShingle | Glowinski, Roland 1937-2022 Numerical methods for nonlinear variational problems Nichtlineare Gleichung (DE-588)4455337-7 gnd Nichtlineare Variationsungleichung (DE-588)4171762-4 gnd Nichtlineares Variationsproblem (DE-588)4234622-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Variationsrechnung (DE-588)4062355-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| subject_GND | (DE-588)4455337-7 (DE-588)4171762-4 (DE-588)4234622-8 (DE-588)4128130-5 (DE-588)4062355-5 (DE-588)4042805-9 (DE-588)4187420-1 |
| title | Numerical methods for nonlinear variational problems |
| title_auth | Numerical methods for nonlinear variational problems |
| title_exact_search | Numerical methods for nonlinear variational problems |
| title_full | Numerical methods for nonlinear variational problems Roland Glowinski |
| title_fullStr | Numerical methods for nonlinear variational problems Roland Glowinski |
| title_full_unstemmed | Numerical methods for nonlinear variational problems Roland Glowinski |
| title_short | Numerical methods for nonlinear variational problems |
| title_sort | numerical methods for nonlinear variational problems |
| topic | Nichtlineare Gleichung (DE-588)4455337-7 gnd Nichtlineare Variationsungleichung (DE-588)4171762-4 gnd Nichtlineares Variationsproblem (DE-588)4234622-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Variationsrechnung (DE-588)4062355-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| topic_facet | Nichtlineare Gleichung Nichtlineare Variationsungleichung Nichtlineares Variationsproblem Numerisches Verfahren Variationsrechnung Numerische Mathematik Variationsungleichung |
| url | http://d-nb.info/840728042/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029758783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT glowinskiroland numericalmethodsfornonlinearvariationalproblems |