Mathematical analysis and numerical methods for science and technology: 6 Evolution problems II
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London
Springer-Verlag
2000
|
| Edition: | [Nachdr.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 485 S. graph. Darst. |
| ISBN: | 3540661026 |
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MARC
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| 100 | 1 | |a Dautray, Robert |d 1928- |0 (DE-588)133309347 |4 aut | |
| 240 | 1 | 0 | |a Analyse mathématique et calcul numérique pour les sciences et les techniques |
| 245 | 1 | 0 | |a Mathematical analysis and numerical methods for science and technology |n 6 |p Evolution problems II |c Robert Dautray ; Jacques-Louis Lions |
| 250 | |a [Nachdr.] | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London |b Springer-Verlag |c 2000 | |
| 300 | |a XII, 485 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Analyse mathématiques |2 ram | |
| 650 | 7 | |a Analyse numérique |2 ram | |
| 650 | 7 | |a Equations d'évolution non linéaires - Solutions numériques |2 ram | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |0 (DE-588)124055397 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008787862 | ||
Record in the Search Index
| _version_ | 1804127597304479744 |
|---|---|
| adam_text | Table
of
Contents
Chapter
XIX.
The Linearised
Navier
Stokes Equations
Introduction
.....................................
і
§1.
The Stationary Navier-Stokes Equations: The Linear Case
....... 1
1.
Functional Spaces
.............................. 2
2.
Existence and Uniqueness Theorem
................... 11
3.
The Problem of
Ľ
Regularity
....................... 18
§2.
The Evolutionary Navier-Stokes Equations: The Linear Case
..... 21
1.
Functional Spaces and Trace Theorems
................. 21
2.
Existence and Uniqueness Theorem
................... 25
3.
/^-Regularity Result
............................ 28
§3.
Additional Results and Review
........................ 31
1.
The Variational Approach
......................... 31
2.
The Functional Approach
......................... 31
3.
The Problem of L Regularity for the Evolutionary
Navier-Stokes Equations: The Linearised Case
............ 33
Chapter XX. Numerical Methods for Evolution Problems
§1.
General Points
................................. 35
1.
Discretisation in Space and Time
.................... 35
2.
Convergence, Consistency and Stability
................ 36
3.
Equivalence Theorem
........................... 37
4.
Comments
.................................. 39
5.
Schemes with Constant Coefficients and Step Size
.......... 40
6.
The Symbol of a Difference Scheme
.................. 41
7.
The
von
Neumann Stability Condition
................. 42
8.
The Kreiss Stability Condition
..................... 43
9.
The Case of Multilevel Schemes
..................... 44
10.
Characterisation of a Scheme of Order
q
............... 44
§2.
Problems of First Order in Time
....................... 45
1.
Introduction
................................. 45
ди д2и
2.
Model Equation
---------=· = 0
for xeR
................. 46
4
дї дх2
χ
Table of Contents
3.
The Boundary Value Problem for Equation
-—
-г—г
= 0...... 54
dt
Sx1
4.
Equation with Variable Coefficients and Schemes with Variable
Step-Size
................................... 56
5.
The Heat Flow Equation in Two Space Dimensions
......... 59
6.
Alternating Direction and Fractional Step Methods
.......... 62
7.
Internal Approximation Schemes
..................... 65
8.
Integration of Systems of Stiff Differential Equations
......... 68
9.
Comments
.................................. 74
§3.
Problems of Second Order in Time
..................... 75
1.
Introduction
................................. 75
2.
The Model Equation
— -
c2 -^
= 0
for xeU
............ 76
3.
The Wave Equation in Two Space Dimensions
............ 82
4.
Internal Approximation Schemes
..................... 84
5.
The Newmark Scheme
........................... 86
6.
The Wave Equation with Viscosity
.................... 90
7.
The Wave Equation Coupled to a Heat Flow Equation
....... 92
8.
Comments
.................................. 95
§4.
The Advection Equation
............................ 96
1.
Introduction
................................. 96
2.
Some Explicit Schemes for the Cauchy Problem in One Space
Dimension
.................................. 97
3.
Positive-Type Schemes and Stable Schemes in LX(K)
......... 105
4.
Some Explicit Schemes
........................... 108
5.
The Problem with Boundary Conditions
................
HO
6.
Phase and Amplitude Error. Schemes of Order Greater than Two
. 113
7.
Nonlinear Schemes for the Equation
-----
ь
α
— = 0.......... 118
õt
дх
8.
Difference Schemes for the Cauchy Problem with Many Space
Variables
................................... 121
§5.
Symmetric
Friedrichs
Systems
........................ 125
1.
Introduction
................................. 125
2.
Summary of Symmetric
Friedrichs
Systems
............... 125
3.
Finite Difference Schemes for the Cauchy Problem
.......... 128
4.
Approximation of Boundary Conditions in the Case where
Ω
=
]0,
1 [ 131
5.
Maxwell s Equations
............................ 132
6.
Remarks
................................... 136
§6.
The Transport Equation
............................ 137
1.
Introduction
................................. 137
2.
Stationary Equation in One-Dimensional Plane Geometry
...... 139
3.
The Evolution Equation in One-Dimensional Plane Geometry
. . . 143
4.
The Equation in One-Dimensional Spherical Geometry
....... 146
Table
of
Contents
XI
5.
Iterative
Solution
of Schemes Approximating the Transport Equation
150
6.
The Two-Dimensional Equation
..................... 154
7.
Other Methods
............................... 158
8.
Comments
.................................. 166
§7.
Numerical Solution of the Stokes Problem
................. 167
1.
Setting of Problem
............................. 167
2.
An Integral Method
............................. 173
3.
Some Finite Difference Methods
..................... 177
4.
Finite Element Methods
.......................... 183
5.
Some Methods Using the Stream Function
............... 194
6.
The Evolutionary Stokes Problem
.................... 200
Chapter
XXI.
Transport
§1.
Introduction. Presentation of Physical Problems
............. 209
1.
Evolution Problems in Neutron Transport
............... 209
2.
Stationary Problems
............................ 213
3.
Principal Notation
............................. 215
§2.
Existence and Uniqueness of Solutions of the Transport Equation.
. . 215
1.
Introduction
................................. 215
2.
Study of the Advection Operator A
=
-v. V
.............. 218
3.
Solution of the Cauchy Transport Problem
.............. 226
4.
Solution of the Stationary Transport Problem in the
Subcriticai Case
240
Summary
..................................... 248
Appendix of
§2.
Boundary Conditions in Transport Problems.
Reflection Conditions
............................. 249
§3.
Spectral Theory and Asymptotic Behaviour of the Solutions
of Evolution Problems
............................. 262
1.
Introduction
................................. 262
2.
Study of the Spectrum of the Operator
В
=
-v.
V-
Σ
........ 265
3.
Study of the Spectrum of the Transport Operator in an Open
Bounded Set X of
W
............................ 272
4.
Positivity
Properties
............................ 285
5.
The Particular Case where All the Eigenvalues are Real
....... 296
6.
The Spectrum of the Transport Operator in a Band.
The Lehner-Wing Theorem
........................ 301
7.
Study of the Spectrum of the Transport Operator in the
Whole Space: X
=
R
............................ 306
8.
The Spectrum of the Transport Operator
ол
the Exterior
of an Obstacle
............................... 321
9.
Some Remarks on the Spectrum of
Г
.................. 324
Summary
..................................... 334
Appendix of
§3.
The Conservative Milne Problem
............ 335
XII Table of
Contents
§4.
Explicit Examples
............................... 347
1.
The Stationary
Transport Problem
in the Whole Space
R
...... 347
2.
The Evolutionary Transport Problem in the Whole Space
...... 352
3.
The Stationary Transport Problem in the Half-Space by the
Method of Invariant Embedding
.................... 355
4.
Case s Method of Generalised Eigenfunctions . Application to
the Critical Dimension in the Case of a Band
............. 363
§5.
Approximation of the Neutron Transport Equation by the
Diffusion Equation
............................... 368
1.
Physical Introduction
........................... 368
2.
Approximation in the Case of a Monokinetic Model of
Evolution Equations and of Stationary Transport Equations
.... 372
3.
Generalisation of Section
2........................ 383
4.
Calculation of a Corrector for the Stationary Problem and
Extrapolation Length
........................... 388
5.
Convergence of the Principal Eigenvalue of the Transport Operator
394
6.
Calculation of a Corrector for the Principal Eigenvalue of the
Transport Operator
............................ 398
7.
Application to a Critical Size Problem
................. 403
8.
Numerical Example in the Case of a Band
............... 405
Appendix of
§5................................. 408
Bibliography
..................................... 417
Perspectives
..................................... 425
Orientation for the Reader
............................ 426
List of Equations
.................................. 429
Table of Notations
................................. 431
Cumulative Index of Volumes
1-6........................ 447
Contents of Volumes
1-5............................. 481
|
| any_adam_object | 1 |
| author | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 |
| author_GND | (DE-588)133309347 (DE-588)124055397 |
| author_facet | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 |
| author_role | aut aut |
| author_sort | Dautray, Robert 1928- |
| author_variant | r d rd j l l jll |
| building | Verbundindex |
| bvnumber | BV012910753 |
| ctrlnum | (OCoLC)44551967 (DE-599)BVBBV012910753 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | [Nachdr.] |
| format | Book |
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| id | DE-604.BV012910753 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:53Z |
| institution | BVB |
| isbn | 3540661026 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008787862 |
| oclc_num | 44551967 |
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| physical | XII, 485 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer-Verlag |
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| spelling | Dautray, Robert 1928- (DE-588)133309347 aut Analyse mathématique et calcul numérique pour les sciences et les techniques Mathematical analysis and numerical methods for science and technology 6 Evolution problems II Robert Dautray ; Jacques-Louis Lions [Nachdr.] Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London Springer-Verlag 2000 XII, 485 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse mathématiques ram Analyse numérique ram Equations d'évolution non linéaires - Solutions numériques ram Lions, Jacques-Louis 1928-2001 (DE-588)124055397 aut (DE-604)BV013031479 6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008787862&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 Mathematical analysis and numerical methods for science and technology Analyse mathématiques ram Analyse numérique ram Equations d'évolution non linéaires - Solutions numériques ram |
| title | Mathematical analysis and numerical methods for science and technology |
| title_alt | Analyse mathématique et calcul numérique pour les sciences et les techniques |
| title_auth | Mathematical analysis and numerical methods for science and technology |
| title_exact_search | Mathematical analysis and numerical methods for science and technology |
| title_full | Mathematical analysis and numerical methods for science and technology 6 Evolution problems II Robert Dautray ; Jacques-Louis Lions |
| title_fullStr | Mathematical analysis and numerical methods for science and technology 6 Evolution problems II Robert Dautray ; Jacques-Louis Lions |
| title_full_unstemmed | Mathematical analysis and numerical methods for science and technology 6 Evolution problems II Robert Dautray ; Jacques-Louis Lions |
| title_short | Mathematical analysis and numerical methods for science and technology |
| title_sort | mathematical analysis and numerical methods for science and technology evolution problems ii |
| topic | Analyse mathématiques ram Analyse numérique ram Equations d'évolution non linéaires - Solutions numériques ram |
| topic_facet | Analyse mathématiques Analyse numérique Equations d'évolution non linéaires - Solutions numériques |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008787862&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013031479 |
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