Finite element approximation of the Navier-Stokes equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1981
|
| Ausgabe: | Rev. repr. of the 1. ed. |
| Schriftenreihe: | Lecture notes in mathematics
749 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 202 S. graph. Darst. |
| ISBN: | 3540095578 0387095578 |
Internformat
MARC
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| 100 | 1 | |a Girault, Vivette |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Finite element approximation of the Navier-Stokes equations |c V. Girault ; P.-A. Raviart |
| 250 | |a Rev. repr. of the 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1981 | |
| 300 | |a VII, 202 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 749 | |
| 650 | 7 | |a Navier-Stokes, Équations de - Solutions numériques |2 ram | |
| 650 | 7 | |a Écoulement visqueux |2 ram | |
| 650 | 7 | |a Éléments finis, Méthode des |2 ram | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Navier-Stokes equations |x Numerical solutions | |
| 650 | 4 | |a Viscous flow | |
| 650 | 0 | 7 | |a Intubation |0 (DE-588)4162196-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Künstliche Beatmung |0 (DE-588)4033439-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |D s |
| 689 | 0 | 1 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
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| 700 | 1 | |a Raviart, Pierre-Arnaud |e Verfasser |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 749 |w (DE-604)BV000676446 |9 749 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-004852461 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804121750964797440 |
|---|---|
| adam_text | CONTENTS
CHAPTER
I.
MATHEMATICAL
FOUNDATION
OF
THE
STOKES
PROBLEM
..............
1
§
1.
GENERALITIES
ON
SOME
ELLIPTIC
BOUNDARY
VALUE
PROBLEMS
............
1
1.1.
BASIC
CONCEPTS
ON
SOBOLEV
SPACES
..............................
1
1.2.
ABSTRACT
ELLIPTIC
THEORY......................................
5
1.3.
EXAMPLE
1
:
DIRICHLET S
HARMONIC
PROBLEM
......................
6
1.4.
EXAMPLE
2
:
NEUMANN S
HARMONIC
PROBLEM........................
8
1.5.
EXAMPLE
3
:
DIRICHLET S
BIHARMONIC
PROBLEM
....................
11
§
2.
SOME
FUNCTION
SPACES
.............................................
12
2.1.
THE
SPACE
H(DIV
;
1)
.........................................
13
2.2.
THE
SPACE
H(CURL
;
0)
........................................
19
§3.
A
DECOMPOSITION
OF
VECTOR
FIELDS
.................................
22
3.1.
EXISTENCE
OF
THE
STREAM
FUNCTION
OF
A
DIVERGENCE-FREE
VECTOR
FIELD
.........................................................
22
3.2.
A
DECOMPOSITION
OF
[L
2
(FT)]
N
...........................
29
3.3.
A
DECOMPOSITION
OF
[H*(0)]
N
..................................
32
§
4.
ANALYSIS
OF
AN
ABSTRACT
VARIATIONAL
PROBLEM
......................
39
4.1.
STATEMENT
AND
SOLUTION
OF
THE
PROBLEM.........................
39
4.2.
A
SADDLE-POINT
APPROACH.......................................
43
4.3.
NUMERICAL
SOLUTION
BY
REGULARIZATION
..........................
45
4.4.
NUMERICAL
SOLUTION
BY
DUALITY
.................................
47
§
5.
THEORY
OF
THE
STOKES
PROBLEM
.....................................
50
5.1.
THE
VELOCITY-PRESSURE
FORMULATION.........................
50
5.2.
THE
STREAM
FUNCTION
FORMULATION...........................
55
VI
CHAPTER
II.
NUMERICAL
SOLUTION
OF
THE
STOKES
PROBLEM.
A
CLASSICAL
METHOD
..
58
§
1.
AN
ABSTRACT
APPROXIMATION
RESULT
.................................
58
§
2.
A
FIRST
METHOD
FOR
SOLVING
THE
STOKES
PROBLEM
......................
64
2.1.
THE
GENERAL
APPROXIMATION
......................................
64
2.2.
EXAMPLE
1
:
A
FIRST-ORDER
APPROXIMATION
........................
70
2.3.
EXAMPLE
2
:
A
SECOND-ORDER
APPROXIMATION.......................
78
2.4.
NUMERICAL
SOLUTION
BY
REGULARIZATION
...........................
83
CHAPTER
III.
A
MIXED
FINITE
ELEMENT
METHOD
FOR
SOLVING
THE
STOKES
PROBL
E
M
.
86
§
1.
MIXED
APPROXIMATION
OF
AN
ABSTRACT
PROBLEM
.........................
86
1.1.
A
MIXED
VARIATIONAL
PROBLEM
....................................
86
1.2.
ABSTRACT
MIXED
APPROXIMATION
...................................
89
§
2.
APPLICATION
TO
THE
HOMOGENEOUS
STOKES
PROBLEM
.....................
93
2.1.
A
MIXED
FORMULATION
OF
STOKES
EQUATIONS
.......................
93
2.2.
A
MIXED
METHOD
FOR
STOKES
PROBLEM.............................
98
2.3.
APPLICATION
TO
FINITE
ELEMENTS
OF
DEGREE
L
...................
101
CHAPTER
IV.
THE
STATIONARY
NAVIER-STOKES
EQUATIONS
.......................
104
§
1.
A
CUSS
OF
NON-LINEAR
PROBLEMS
....................................
104
§
2.
APPLICATION
TO
THE
NAVIER-STOKES
EQUATIONS
........................
110
2.1.
SOME
RESULTS
OF
FUNCTIONAL
ANALYSIS
...........................
110
2.2.
SOLUTIONS
OF
THE
NAVIER-STOKES
PROBLEM
........................
113
§
3.
A
FIRST
METHOD
FOR
APPROXIMATING
THE
NAVIER-STOKES
EQUATIONS
......
121
3.1.
THE
UNIQUENESS
CASE
.............................
121
3.2.
THE
NON-UNIQUENESS
CASE
.......................................
127
§
4.
A
MIXED
METHOD
FOR
APPROXIMATING
THE
NAVIER-STOKES
PROBLEM
........
135
4.1.
A
MIXED
FORMULATION
...........................................
135
4.2.
AN
ABSTRACT
MIXED
APPROXIMATION
...............................
138
4.3.
APPLICATIONS
..................................................
143
VII
CHAPTER
V.
THE
TIME-DEPENDENT
NAVIER-STOKES
EQUATIONS
...................
148
§
1.
THE
CONTINUOUS
PROBLEM
.........................................
148
1.1.
SOME
VECTOR-VALUED
FUNCTION
SPACES
...........................
148
1.2.
FORMULATION
OF
THE
NAVIER-STOKES
PROBLEM
.....................
154
1.3.
EXISTENCE
AND
UNIQUENESS
OF
THE
SOLUTION.....................
161
§
2.
NUMERICAL
SOLUTION
BY
SEMI-DISCRETIZATION
:
A
ONE-STEP
METHOD
...
170
§
S.
SEMI-DISCRETIZATION
WITH
A
MULTISTEP
METHOD
.....................
179
3.1.
GENERALITIES
ABOUT
MULTISTEP
METHODS
.........................
179
3.2.
MULTISTEP
METHODS
FOR
SOLVING
THE
NAVIER-STOKES
PROBLEM
......
182
3.3.
CONVERGENCE
OF
A
FAMILY
OF
TWO-STEP
METHODS
..................
185
BIBLIOGRAPHICAL
NOTES
.....................................................
192
REFERENCES
................................................................
195
INDEX.....................................................................
200
APPENDIX
..................................................................
201
|
| any_adam_object | 1 |
| author | Girault, Vivette Raviart, Pierre-Arnaud |
| author_facet | Girault, Vivette Raviart, Pierre-Arnaud |
| author_role | aut aut |
| author_sort | Girault, Vivette |
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| bvnumber | BV007473983 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)10917035 (DE-599)BVBBV007473983 |
| discipline | Mathematik |
| edition | Rev. repr. of the 1. ed. |
| format | Book |
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| id | DE-604.BV007473983 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:02:57Z |
| institution | BVB |
| isbn | 3540095578 0387095578 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004852461 |
| oclc_num | 10917035 |
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| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 |
| physical | VII, 202 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Girault, Vivette Verfasser aut Finite element approximation of the Navier-Stokes equations V. Girault ; P.-A. Raviart Rev. repr. of the 1. ed. Berlin [u.a.] Springer 1981 VII, 202 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 749 Navier-Stokes, Équations de - Solutions numériques ram Écoulement visqueux ram Éléments finis, Méthode des ram Finite element method Navier-Stokes equations Numerical solutions Viscous flow Intubation (DE-588)4162196-7 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Künstliche Beatmung (DE-588)4033439-9 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s Finite-Elemente-Methode (DE-588)4017233-8 s 1\p DE-604 Intubation (DE-588)4162196-7 s Künstliche Beatmung (DE-588)4033439-9 s DE-604 Raviart, Pierre-Arnaud Verfasser aut Lecture notes in mathematics 749 (DE-604)BV000676446 749 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004852461&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Girault, Vivette Raviart, Pierre-Arnaud Finite element approximation of the Navier-Stokes equations Lecture notes in mathematics Navier-Stokes, Équations de - Solutions numériques ram Écoulement visqueux ram Éléments finis, Méthode des ram Finite element method Navier-Stokes equations Numerical solutions Viscous flow Intubation (DE-588)4162196-7 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Künstliche Beatmung (DE-588)4033439-9 gnd |
| subject_GND | (DE-588)4162196-7 (DE-588)4041456-5 (DE-588)4017233-8 (DE-588)4033439-9 |
| title | Finite element approximation of the Navier-Stokes equations |
| title_auth | Finite element approximation of the Navier-Stokes equations |
| title_exact_search | Finite element approximation of the Navier-Stokes equations |
| title_full | Finite element approximation of the Navier-Stokes equations V. Girault ; P.-A. Raviart |
| title_fullStr | Finite element approximation of the Navier-Stokes equations V. Girault ; P.-A. Raviart |
| title_full_unstemmed | Finite element approximation of the Navier-Stokes equations V. Girault ; P.-A. Raviart |
| title_short | Finite element approximation of the Navier-Stokes equations |
| title_sort | finite element approximation of the navier stokes equations |
| topic | Navier-Stokes, Équations de - Solutions numériques ram Écoulement visqueux ram Éléments finis, Méthode des ram Finite element method Navier-Stokes equations Numerical solutions Viscous flow Intubation (DE-588)4162196-7 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Künstliche Beatmung (DE-588)4033439-9 gnd |
| topic_facet | Navier-Stokes, Équations de - Solutions numériques Écoulement visqueux Éléments finis, Méthode des Finite element method Navier-Stokes equations Numerical solutions Viscous flow Intubation Navier-Stokes-Gleichung Finite-Elemente-Methode Künstliche Beatmung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004852461&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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