Mathematical analysis and numerical methods for science and technology: 4 Integral equations and numerical methods
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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: | X, 495 S. graph. Darst. |
| ISBN: | 354066100X |
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MARC
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| 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 4 |p Integral equations and numerical methods |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 X, 495 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 7 | |a Analyse mathématique |2 ram | |
| 650 | 7 | |a Analyse numérique |2 ram | |
| 650 | 7 | |a Equations intégrales - Solutions numériques |2 ram | |
| 700 | 1 | |a Artola, Michel |e Sonstige |4 oth | |
| 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:BVB01-008878225 | ||
Record in the Search Index
| _version_ | 1804127728395354112 |
|---|---|
| adam_text | Table
of
Contents
Chapter X. Mixed Problems and the
Tricomi
Equation
Introduction
.......................... 1
§ 1.
Description and Formulation of the Problem
.......... 2
1.
Stationary Plane Flow of a Compressible Fluid
........ 2
2.
Solution in the Hodograph Plane; The
Franki
Equation
.... 9
§ 2.
Methods for Solving Problems of Mixed Type
......... 15
1.
An Example of a Well-Posed Boundary Value Problem
for the
Franki
Equation
................. 15
2.
Particular Solutions
................... 21
3.
Existence and Uniqueness Results
............. 23
Bibliographic Commentary
................... 31
Chapter XI. Integral Equations
Introduction
.......................... 33
Part A. Solution Methods Using Analytic Functions and Sectionally
Analytic Functions
.................... 38
Introduction
.......................... 38
§1.
The
Wiener-Hopf
Method
.................. 38
Introduction.
Wiener-Hopf
Equations
............. 38
1.
The
Wiener-Hopf
Method
................. 39
2.
Decomposition of an Analytic Function Defined in a Strip
in the Complex Plane
................... 42
3.
Factorisation of an Analytic Function Defined in a Strip
in the Complex Plane
................... 43
4.
Application to the
Wiener-Hopf
Integral Equation
of the Second Kind
.................... 45
5.
Application to the Milne Problem
............. 47
6.
Application to the Dock Problem
.............. S3
VIII Table of
Contents
§ 2.
Sectionałly
Analytic Functions
................ 57
Introduction
........................ 57
1.
S.
Analytic Functions
................... 58
2.
Cauchy Integrals and Plemelj Formulas
........... 59
3.
The
Poincaré-Bertrand
Formula and the Hubert
Inversion Formula
.................... 65
§ 3.
The Hubert Problem
.................... 74
Introduction
........................ 74
1.
The Hubert Problem in the Case where
L
is a Contour
.... 74
2.
The Hilbert Problem in the Case where
L
is an Arc
...... 77
3.
The Hilbert Problem in the Case of a Straight Line
...... 81
4.
Some Problems Reducible to a Hilbert Problem
....... 83
§ 4.
Application to Some Problems in Physics
........... 91
Introduction
........................ 91
1.
Simple Layer and Double Layer Problems
.......... 91
2.
Determination of the Charge Density on the Surface
of a Cylindrical Body at Potential V
............ 93
3.
The Problem of the Thin Aerofoil Profile
.......... 97
4.
Plane Elasticity and the Biharmonic Equation
........ 103
Part B. Integral Equations Associated with Elliptic Boundary
Value Problems in Domains in R3
.............
§1.
Study of Certain Weighted Soboiev Spaces
........... 114
Introduction
........................ 114
§ 2.
Integral Equations Associated with the Boundary Value Problems
of Electrostatics
...................... 119
1.
Integral Representations
................. 119
2.
Dirichlet Problems Relative to the Operator
Δ
........ 122
3.
Neumann Problems Relative to the Operator A
........ 130
§ 3.
Integral Equations Associated with the
Heimholte
Equation
. . . 141
§ 4.
Integral Equations Associated with Problems of Linear Elasticity
. 148
§5.
Integral Equations Associated with the Stokes System
...... 152
Chapter
ΧΠ.
Numerical Methods for Stationary Problems
Introduction
.......................... 160
1.
The Basic Ideas of Finite Difference Methods and Finite
Element Methods
.................... 160
2.
Comparison of the Two Methods. Field of Applications
of the Finite Element Method
............... 168
Table
of Contents IX
3.
The Different Topics Treated in this Chapter
XII
....... 170
4.
The Lax-
Milgram
Theorem and Sobolev Spaces
....... 171
§ 1.
Principal Aspects of the Finite Element Method Applied
to the Problem of Linear Elasticity
.............. 173
1.
Variational Formulation of the Continuous Problem
..... 173
2.
Construction of Approximation Function Spaces
....... 179
3.
The First Approximation Problem (Phl)
........... 192
4.
Numerical Quadrature Schemes and the Definition
of the Second Approximation Problem
(Pk2)
......... 194
5.
Error Estimates
..................... 197
6.
Numerical Implementation
................ 229
§ 2.
Treatment of Domains with Curved Boundaries
......... 240
1.
Exact
Triangulation
of the Domain
Ω
........... 241
2.
Construction of an Approximate
Triangulation
of the Domain
Ω
242
3.
Examples of the Construction of the Mappings FK
...... 249
4.
Definition of Curved Finite Elements of Class ^°
....... 251
5.
Estimation of the Interpolation Error
............ 256
6.
Application to the Solution of the Problem of Plane
Linear Elasticity
..................... 257
§ 3.
A Non
Conforming Method of Finite Elements
......... 271
1.
The Wilson Finite Element
................ 272
2.
Estimation of the Interpolation Error
............ 272
3.
The Space Xh of Finite Elements
.............. 275
4.
The Discrete Problem. Abstract Error Estimate
........ 276
5.
The Bilinear Lemma
................... 285
6.
Estimation of the Error ||
й-щ к
.............. 286
§ 4.
Applications to the Problems of Plates and Shells
........ 290
1.
Approximation of the Problems of Plates
.......... 291
2.
Approximation of the Problems of Shells
.......... 301
§5.
Approximation of Eigenvalues and Eigenvectors
........ 316
1.
Some Results from the Spectral Theory of Differential Operators
317
2.
The Approximate Problem
................ 320
3.
Estimation of the Errors |
Лј—Дџ
|, i^j^3Mh
........ 323
4.
Estimation of the Errors || uruhj||,1
</<3
M„
........
328
5.
Numerical Solutions
................... 331
§ 6.
An Example of the Approximate Calculation for a Problem
of the Eigenvalues of
a Non Self-Adjoint
Operator
....... 332
1.
The Neutron Diffusion Equations Recalled
......... 332
2.
The Critical Problem with Two Energy Groups
........ 334
3.
Determination of the Positive Solution
........... 339
4.
Extension to the Case Where the Number of Neutron (Kinetic)
Energy Groups is Greater than Two
............ 345
χ
Table of Contents
5.
The Eigenvalue Problem Connected with the Evolution Problem
of Neutron Diffusion
................... 349
6.
Some Comments
..................... 356
Review of Chapter
XII..................... 357
Chapter
ХШ.
Approximation of Integral Equations by Finite Elements.
Error Analysis
Introduction
.......................... 359
§1.
The Case of a Polyhedral Surface
............... 359
1.
The Simple Layer Potential Case for the Dirichlet Problem
. . . 359
2.
Study of the Potential of a Double Layer
for the Neumann Problem in R3
.............. 362
3.
Study of the Exterior Neumann Problem Represented
by a Simple Layer
.................... 364
§ 2.
The Case of a Regular Closed Surface
............. 367
1.
The Approximation of Surfaces
.............. 367
2.
Notions on the Error Generated by the Approximation
of the Surface
...................... 368
Appendix. Singular Integrals
Introduction
.......................... 371
§1.
Operator, Convolution Operator, Integral Operator
....... 371
§ 2.
The Hubert Transformation
................. 382
§ 3.
Generalities on Singular Integral Operators
........... 393
§ 4.
Operators with Symbols, Operators on L2
........... 403
§5.
The Calderon-Zygmund Theorem
............... 409
§ 6.
Marcinkiewicz Spaces
.................... 414
1.
Definitions
....................... 414
2.
Application to the Homogeneous Convolution Kernel
..... 417
3.
The Hubert Transformation in the Space
Lł(R)
....... 418
4.
Operators of Weak Type. The Marcinkiewicz Theorem
.... 421
5.
The Maximal Hardy-Littlewood Operator.
Proof of Lemma
1
in
§2 ................. 424
Bibliography
.......................... 427
Table of Notations
....................... 441
Index
............................. 455
Contents of Volumes
1-3, 5,6.................. 489
|
| 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 | BV013031480 |
| ctrlnum | (OCoLC)44551965 (DE-599)BVBBV013031480 |
| 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.BV013031480 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:58Z |
| institution | BVB |
| isbn | 354066100X |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008878225 |
| oclc_num | 44551965 |
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| owner_facet | DE-703 DE-355 DE-BY-UBR DE-20 |
| physical | X, 495 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 4 Integral equations and numerical methods Robert Dautray ; Jacques-Louis Lions [Nachdr.] Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London Springer-Verlag 2000 X, 495 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse mathématique ram Analyse numérique ram Equations intégrales - Solutions numériques ram Artola, Michel Sonstige oth Lions, Jacques-Louis 1928-2001 (DE-588)124055397 aut (DE-604)BV013031479 4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878225&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 mathématique ram Analyse numérique ram Equations intégrales - 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 4 Integral equations and numerical methods Robert Dautray ; Jacques-Louis Lions |
| title_fullStr | Mathematical analysis and numerical methods for science and technology 4 Integral equations and numerical methods Robert Dautray ; Jacques-Louis Lions |
| title_full_unstemmed | Mathematical analysis and numerical methods for science and technology 4 Integral equations and numerical methods 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 integral equations and numerical methods |
| topic | Analyse mathématique ram Analyse numérique ram Equations intégrales - Solutions numériques ram |
| topic_facet | Analyse mathématique Analyse numérique Equations intégrales - Solutions numériques |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013031479 |
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