Numerical analysis of variational inequalities:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English French |
| Published: |
Amsterdam [u.a.]
North-Holland
1981
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| Series: | Studies in mathematics and its applications
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIX, 776 S. graph. Darst. |
| ISBN: | 0444861998 |
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MARC
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| 100 | 1 | |a Glowinski, Roland |d 1937-2022 |e Verfasser |0 (DE-588)120514737 |4 aut | |
| 240 | 1 | 0 | |a Analyse numérique des inéquations variationnelles |
| 245 | 1 | 0 | |a Numerical analysis of variational inequalities |c Roland Glowinski ; Jacques-Louis Lions ; Raymond Trémolières |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1981 | |
| 300 | |a XXIX, 776 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Studies in mathematics and its applications |v 8 | |
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Inégalités différentielles | |
| 650 | 4 | |a Differential inequalities | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Variational inequalities (Mathematics) | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
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| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |e Verfasser |0 (DE-588)124055397 |4 aut | |
| 700 | 1 | |a Trémolières, Raymond |e Verfasser |4 aut | |
| 830 | 0 | |a Studies in mathematics and its applications |v 8 |w (DE-604)BV000000646 |9 8 | |
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Record in the Search Index
| _version_ | 1804116534224748544 |
|---|---|
| adam_text | TABLE OF CONTENTS
Chapter 1 : General methods of approximation for
steady state inequality problems l
Synopsis 1
1. Examp les 1
1.1 Fluid mechanics problems in media with semi
permeable boundaries 1
1.2 Model elasto plastic problem 6
1.3 Model friction problem 7
1.1+ A flow problem 9
1.5 Synopsis 10
2. Geneva! formulation of steady state variational
inequalities 10
2.1 The symmetric case 10
2.2 The nonsymmetric case , 13
2.3 Synopsis 1?
3. Infinite dimensional approximation methods 15
3.1 Successive approximations 15
3.2 Penalisation 19
3.3 Regularisation 21
3.1+ Duality (I) 22
3 • 5 Duality (II) 26
3.6 Duality (III) 31
3.7 Various remarks 36
3.8 Synopsis 37
h. Interior approximations 37
l+.l Interior approximations of V. Finite elements ... 37
1+.2 Interior approximation schemes in the case
of equations kO
h. 3 Approximations of K 1+1
1+.1+ Approximation schemes for the initial problem .... 1+1
1+.5 Approximation schemes for the penalised or
regularised problems 1+3
1+.6 Approximation schemes for the dual problem ........ 1+1+
1+.7 Open problems. Estimates of the approximation
error k6
5. Exterior approximations 1+9
5.1 An example ^9
5.2 Exterior approximations for V3 a3 K3 j 52
5.3 Exterior approximation schemes 55
6. Conclusions 57
Chapter 2 : Optimisation algorithms 59
Synopsis 59
1. The relaxation method 59
1.1 Description of the point relaxation method.
Unconstrained case 59
1.2 Point relaxation. Constrained case 6h
1.3 Block relaxation 66
l.U Over relaxation and under relaxation 67
1.5 A class of nondifferentiahle functionals which
can be minimised using relaxation 71
2. Methods of the gradient and gradient projection type .. 75
2.1 General remarks 75
2.2 Methods of the gradient type (unconstrained
case) 75
2.3 Methods of the conjugate gradient type
(unconstrained case) 76
2. h Constrained case 79
3• Penalty methods and variants 8l
3.1 General remarks 81
3.2 Interior methods 81
3.3 Exterior methods 83
3.^ Method of centres with variable truncation 85
h. Duality methods 89
h. 1 General remarks 89
h. 2 Examples 90
k.3 A saddle point search algorithm 91
l+.lj A second saddle point search algorithm 9^
5. Application of relaxation and duality methods to the
numerical analysis of a model variational problem 97
5.. 1 General remarks 97
5.2 The continuous problem 97
5.3 The approximate problem 99
5.^ Convergence of the approximate solution as h ¦ 0 . 101
5.5 Solution of the approximate problem hy point
over relaxation with constraints 10^+
5.6 Solution hy a duality method 10**
5.7 Analysis of the numerical results 108
6. Discussion 113
Chapter 3 : Numerical analysis of the problem of
the elasto plastic torsion of a
cylindrical bar 117
Introduction 117
1. Statement of the continuous problem. Physical
motivation. Synopsis 117
1.1 Statement of the continuous problem 117
1.2 Physical motivation 118
1.3 Synopsis 119
2. Some properties of the solution of the problem (PQ) .. 120
2.1 Regularity results 120
2.2 An equivalent variational problem 120
2.3 Some particular cases where the solution is
known 121
3. Numerical analysis of the problem (P^) 123
3.1 Synopsis 123
3.2 Exterior approximation of problem (P^) 123
3.3 Convergence of the approximate solution
as h 0 125
3.U Solution of the approximate problem by point
over relaxation with projection 131
3.5 Applications. Example 1 132
3 6 Applications. Example 2 135
h. Interior approximations of (Po) 136
Synopsis 136
U.I A finite element method 137
U.2 An interior approximation method using the
eigenfunctions of the operator A in Hq(°,) li|2
5. Exterior approximations of (Po) 1^5
5.1 Approximations of J lij 5
5.2 Exterior approximations of KQ lU6
5.3 Formulation of the approximate problem 150
5.U Solvability of the approximate problem 150
6. Convergence of the interior and exterior
approximations 150
Synopsis 150
6.1 A lemma concerning density 151
6.2 Convergence of the interior approximations 152
6.3 Convergence of the exterior approximations 157
7. Numerical solution of the approximate problems
relating to (Pp), by relaxation and point over
relaxation with sequential projection 175
7 1 Synopsis 175
7 ¦ 2 Description of the method 175
7.3 Convergence results 179
7. h Applications. Example 1 188
7.5 Applications. Example 2 192
7.6 Applications. Example 3 193
7 ¦ 7 Various remarks 19*+
8. Solution of the approximate problems relating to (Po)
by penalty methods 196
8.1 Synopsis 196
8.2 A first penalty method 197
8.3 A second penalty method 206
8.U Comparisons 218
9 Solution of the approximate problems relating to (Po)
by duality methods 219
9 1 Introduction and synopsis 219
9.2 Application of the duality method. Case of the
finite element approximation of Section k.l .... 22^
9.3 Application of the duality method. Case of the
interior approximation by eigenfunctions of
A in ffj(fi) 231
9.^ Application of the duality method. Case of the
exterior approximations of Section 5 237
9 5 Application of the duality method of Section
9.1 3 to the solution of the approximate
problems 2h
10. Discussion 2h6
Chapter 4 : Thermal control problems, boundary
unilateral problems, and elliptic
variational inequalities of order 4 . 2h9
Synopsis 2U9
1. Problems of thermal control and of the diffusion of
fluids through semi permeable walls 2*i9
1.1 Formulation of the problem 2U9
1.2 Existence and uniqueness results for
problem (1.!+),(!.5) 251
1.3 Approximation by a finite element method 253
I.h Convergence of the approximate solutions, (i)..
The case q = 1 255
1.5 Convergence of the approximate solutions. (il).
The case q = 2 268
1.6 Numerical solution of the approximate problems . 273
1.7 Examples , 278
2. Friction problems 288
2.1 Formulation of the problems 288
2.2 Existence and uniqueness results for problem
(2.1), (2.2) 288
2.3 Relationship with the problems of Section 1 ... 288
2.k Dependence of the solution on g 290
2.5 Duality properties 29^
2.6 Approximation by finite elements 297
2.7 Numerical solution of the approximate problems. 298
2.8 An example 301
3. A problem with unilateral constraints at the
boundary 308
3.1 Synopsis 308
3.2 Existence and uniqueness results for problem
(3.1), (3.2) 308
3.3 Regularity results 308
3. k Duality results 309
3.5 Approximation by finite elements of order one
and two 310
3.6 numerical solution of the approximate problems. 313
3.7 An example 315
k. Numerical analysis of variational inequalities of
order k 317
k.l Synopsis , 317
k.2 An iterative method for solving certain varia¬
tional problems of order k 317
k.3 A new variational formulation of the Dirichlet
problem for A2 328
k.k An iterative method for the solution of the
Dirichlet problem for A2 based on the variat¬
ional formulation given in Section k.3 330
it.5 An approximation of problem (k.2), (k.3) by
mixed finite elements 332
k.6 An iterative method for the solution of the
approximate problem (k.J2). Generalisation to
inequalities of order k 335
k.J Example and numerical application 339
5. Discussion 3^5
Chapter 5 : Numerical analysis of the steady
flow of a Bingham fluid in a
cylindrical duct 3U7
1. Statement of the continuous problem. Physical
motivation. Synopsis 3^7
1.1 Statement of the continuous problem 3^ 7
1.2 Physical motivation 3^+8
1.3 Synopsis 3^8
2. Some properties of the solution of the continuous
problem 3^8
2.1 Regularity results 3^8
2.2 Dependence of the solution on g 3*+8
2.3 Some particular cases for which the solution is
known 352
3. Interior approximation of (P ) by a finite element
method , 355
Synopsis 355
3.1 Triangulation of Q. Definition of V, 355
3.2 Definition of the approximate problem 355
3.3 Solvability of the approximate problem 355
3.^ Explicit formulation of the approximate problem 355
3.5 On the use of finite elements of order greater
than 1 356
k. Exterior approximations of (p ) 357
k. 1 Approximation of JQ 357
k .2 Exterior approximations of j 357
^.3 Formulation of the approximate problem 359
i+.^4 Solvability of the approximate problem 359
5. Convergence of the interior and exterior approx¬
imations 359
Synopsis , 359
5.1 Convergence of the finite element method of
Section 3 360
5 2 Convergence of the exterior approximations .... 36l
6. Methods of solution by regularising j 3.63
Synopsis 363
6.1 Regularisation of the continuous problem (Po) . 36U
6.2 Regularisation of the approximate problems .... 371
6.3 Solution of the regularised approximate
problems, (i). Method of point over relax¬
ation 37*+
6.k Solution of the regularised approximate
problems, (il). Gradient method with auxiliary
operator , 378
7. Duality methods 382
Synopsis 382
7 1 Application to the solution of the continuous
problem 382
7.2 Application to the solution of the approximate
problems, (i). Case of the exterior approx¬
imations of Section k 383
7.3 Application to the solution of the approximate
problems. (II). The case of finite element
approximations 391
8. Application to the solution of the elasto piastic
torsion problem of Chapter 3 398
8.1 Synopsis 398
8.2 Reformulation of algorithm (9 5), (9 6), (9 7)
of Chapter 3, Section 9.1.1 398
8.3 Approximate implementation of algorithm (8.7),
(8.8), (8.9) 399
8.k Application to an example Uoi
8.5 A variant of algorithm (8.13), (8.lU), (8.15) . 1*01
9. Discussion 1+02
Chapter 6 : General methods for the approximation
and solution of time dependent
variational inequalities I1O5
Introduction 1+05
1. Background 1+06
1.1 Spaces of vector valued distributions and
functions lj.06
1.2 Functional setting koj
2. Introduction to parabolic time dependent inequal¬
ities of type I ; ko8
2.1 Examples of parabolic inequalities of type J . . I4.08
2.2 Abstract formulations 1j.^q
3. Approximations of parabolic inequalities of type I . ^.h
Synopsis j_~h
3.1 Fundamental assumptions for the approximation . I4.15
3.2 Approximation schemes for parabolic
inequalities of type I ., I^q
3.3 Convergence of the approximate inequalities ... I4.22
k. Numerical solution of some parabolic inequalities
of type I l+3x
h. 1 A model problem 1^31
k.2 A model problem of time dependent friction .... ^30
k.3 A model problem of the deformation of a
membrane ijW
5 Introduction to parabolic inequalities of type II .. k,
5.1 Example I l^co
5.2 Abstract formulation and existence theorem .... 1^^
6. Approximation of parabolic inequalities of type~n . i^g
6.1 Fundamental assumptions for the approximation . l^g
6.2 Approximation scheme for parabolic inequalities
of type II I4.55
6.3 Convergence of the approximate inequalities ... Wg
7. Numerical solution of parabolic inequalities
of type II U67
7 1 Solution of Example I k69
7 • 2 Solution of Example II i+73
7.3 Conclusions hlk
8. Introduction to time dependent inequalities of the
second order in t hf6
8.1 Example I kj6
8.2 Example II U77
8.3 Abstract formulation kTJ
9. Approximation of inequalities of the second
order in t 1+79
9.1 Assumptions , 1+79
9.2 Approximation schemes l+8l
9.3 Convergence of the approximate inequalities ... U83
10. Numerical solution of inequalities of the second
order in t 1+93
10.1 Solution of Example. I 1+93
10.2 Solution of Example II U95
11. Numerical computation of the flow of Bingham
fluids 1+99
11.1 Notation and statement of the problem 1+99
11.2 Numerical schemes 501
11.3 Numerical results 509
12. Discussion , 517
References 521
Appendix 1 : Further discussion of steady state
inequalities 5I+1
1. Synopsis 5I+I
2. Existence, uniqueness and approximation results
for problems (l.1A) and (l.2A) 5^2
2.1 The functional setting 5^2
2.2 Existence and uniqueness results for
(1.1A) and (1.2A) 5^2
2.3 On the interior approximation of (l.lA)
and (1.2A) 5^5
3. The obstacle problem, (i). General remarks. Con¬
forming approximations 553
3.1 Synopsis 553
3.2 Formulation of the problem. Physical
interpretation 553
3.3 Other phenomena related to the obstacle
problem 55^
3.h Interpretation of (3.1A), (3.2A) as a free
boundary problem 555
3.5 Existence, uniqueness and regularity of the
solution of (3.1A), (3.2A) 556
3.6 Finite element approximations of problem (3.1A),
(3 2A). (i). Piecewise linear approximations ... 556
3.7 Finite element approximations of problem (3.1A),
(3.2A). (II). Piecewise quadratic
approximations 561
h. The obstacle problem. (il). Non conforming
approximations using mixed finite elements 562
U.I Synopsis 562
k.2. A dual formulation of the obstacle problem
(3.1A), (3.2A) 562
k.3 An approximation of the dual problem (U.6A),
(h.7A) by mixed finite elements 563
5. On a stamp problem which leads to a variational
inequality for a pseudo differential operator 565
5.1 Statement of the problem 565
5.2 Functional formulation 566
5.3 Finite element approximation 568
6. Solution of nonlinear Dirichlet problems by reduction
to Vaviational inequalities 569
6.1 Synopsis 569
6.2 The continuous problem , 570
6.3 Existence and uniqueness results for
(6.2A), (6.3A) 571
6.k The finite element approximation of (6.2A),
(6.3A) and (6.8A) 572
7. Introduction to numerical algorithms for quasi
variational inequalities 58l
7.1 Quasi variational inequalities 58l
7.2 Iterative scheme 583
Appendix 2 . Further discussion of optimisation
algorithms 587
1. Synopsis 587
2. The method of block overrelaxation with projection ... 587
2.1 Statement of the problem 588
2.2 Description of the algorithm 589
2.3 Convergence of algorithm (2.10A), (2.11A) 589
2. h Various remarks 590
3. Duality methods a further discussion 590
k. Introduction to complementarity methods 595
h.l General remarks. Synopsis 595
h.2. The obstacle problem from the point of view of
complementarity methods 597
h. 3 Discussion and references 602
5. Minimisation of quadratic functionals over the
products of intervals, using conjugate gradient
methods 603
5.1 Synopsis 603
5.2 Description of the method. Convergence results . 60^
5.3 Discussion 609
6. Alternating direction methods. Application to the
solution of nonlinear variational ¦problems 609
6.1 Formulation of the problem. Synopsis 6l0
6.2 Convergence of algorithms (6.3A), (6.kA) and
(6.5A), (6.6A) 611
6.3 Application to the solution of the obstacle
problem 6l6
7. Relationship between the alternating direction methods
and augmented Lagrangian methods 617
7.1 A model problem in Hilbert space 6l7
7.2 Decomposition coordination of (7 1A), (7 2A)
using the augmented Lagrangian 6l8
7.3 Solution of (7.1A), (7.2A) via duality algorithms
for Lr , 619
T.h An alternating direction interpretation of
algorithms (7.12A) (7.15A) and (T.l6A) (T.20A) .. 621
Appendix 3 : Further discussion of the numerical
analysis of the elasto piastic
torsion problem 623
1. Synopsis , , 623
2. The finiterelement approximation of problem (l.lA)
(l). Error estimates for p ieaewise linear approx¬
imations , 6zh
2.1 One dimensional case .,..,, 62k
2.2 Two dimensional case 626
3. Finite element approximation of problem (l.lA). (II).
Optimal order estimates through the use of an equiv¬
alent formulation ..,,.,......., , 63O
3.1 Equivalent formulation of problem (l.lA) 630
3.2 Approximation of problem (3.1A) by a finite
element method 635
k. Further discussion of iterative methods for solving
the elasto plastic torsion ¦problem 6ho
Ij .l General discussion. Synopsis 6^0
U.2 Solution of problem (3.1A) by a duality method .. Gki
k.3 On conjugate gradient type variants of algorithm
(U.3A) (U.5A) 6h6
Appendix 4 : Further discussion of boundary
unilateral problems and elliptic
variational inequalities of order
4. Application to fluid
mechanics 653
1. Synopsis 653
2. Conforming and non conforming approximations of the
boundary unilateral problem (l.lA), (1.2A) 65k
2.1 Approximation of the unilateral problem (l.lA),
(l.2A) by first order conforming finite elements. 65^
2.2 Approximation of the boundary unilateral problem
(l.lA), (1.2A) using non conforming finite
elements of mixed type 658
3. Further discussion on the approximation of fourth
order variational problems using mixed finite element
methods , 662
3.1 Synopsis , 662
3.2 Further discussion of the convergence of the
mixed finite element method of Chapter k,
Section k.5 662
3.3 Discussion supplementing Chapter h, Section h.6
on the solution of the approximate biharmonic
problem (h.72) 663
3.k Application to the numerical solution of problem
(1.3A), (l.U) 666
h. Numerical simulation of the transonic potential flow
of ideal compressible fluids using variational
inequality methods 690
U.I Synopsis , 69O
k.2 Mathematical formulation 691
U.3 Least squares formulation of the continuous
problem 693
k.h Finite element approximation and least squares
conjugate gradient solution of the approximate
problems ...,.,.......,,.. 695
U.5 Numerical implementation of the entropy
condition , 702
h.6 numerical experiments 709
5. Supplementary bibliography 716
i
i
Appendix 5 : Further discussion of the numerical
analysis of the steady flow of a
Bingham fluid in a cylindrical
duct 717
1. Synopsis 717
2. Finite element approximation of problem (l.lA). (i).
Error estimates for pieoewise linear approximations . 7l8
2.1 One dimensional case 7l8
2.2 Two dimensional case 721
3. Finite element approximations of problem (l.lA). (II).
Optimal order error estimates through the use of an
equivalent formulation 721
3.1 Equivalent formulation of problem (l.lA) 722
3.2 Approximation of problem (3.1A) by a finite
element method 725
k. Supplementary information on iterative methods for
solving the problem of the steady flow of a Bingham
fluid in a cylindrical duct 727
^.1 General discussion. Synopsis 727
k.2 Solution of problem (3.1A) by a duality method . 728
h.3 On conjugate gradient type variants of algorithm
(J+.3A) (1+.5A) 730
Appendix 6 : Further discussion of the numerical
analysis of time dependent
variational inequalities 733
1. Synopsis , , 733
2. Supplementary bibliography ¦ 733
3. On the steady flow of a Bingham fluid in a cylindrical
duct. Asymptotic properties of the continuous and
discrete problems 736
3.1 Formulation of the problem. Existence and
uniqueness results , 736
3.2 On the asymptotic behaviour of the continuous
problem , 737
3.3 Approximation of (3.1A). Asymptotic
properties of the discrete solution 739
3. h Further remarks 7^3
h. Numerical simulation of the flow of a Bingham fluid
in a two dimensional cavity , using a stream function
method 7^3
h.l Synopsis , 7^3
h.2 Review of the velocity formulation of the
Bingham flow problem 7^3
k.3 A stream function formulation of the Bingham
flow problem 7^5
k.k Approximation of the steady state problem 7^7
^ ,5 Approximation of the time dependent problem
(U.15A) 75!+
h.6 Solution of (U.19A), (i|.5i»A) by augmented
Lagrangian methods 756
h.7 Numerical experiments 76l
Bibliography of the Appendices , , 767
|
| any_adam_object | 1 |
| author | Glowinski, Roland 1937-2022 Lions, Jacques-Louis 1928-2001 Trémolières, Raymond |
| author_GND | (DE-588)120514737 (DE-588)124055397 |
| author_facet | Glowinski, Roland 1937-2022 Lions, Jacques-Louis 1928-2001 Trémolières, Raymond |
| author_role | aut aut aut |
| author_sort | Glowinski, Roland 1937-2022 |
| author_variant | r g rg j l l jll r t rt |
| building | Verbundindex |
| bvnumber | BV002082796 |
| callnumber-first | Q - Science |
| callnumber-label | QA374 |
| callnumber-raw | QA374 |
| callnumber-search | QA374 |
| callnumber-sort | QA 3374 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 490 SK 910 SK 920 |
| ctrlnum | (OCoLC)7464810 (DE-599)BVBBV002082796 |
| dewey-full | 515.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/6 |
| dewey-search | 515.3/6 |
| dewey-sort | 3515.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002082796 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:02Z |
| institution | BVB |
| isbn | 0444861998 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001363612 |
| oclc_num | 7464810 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-824 DE-29T DE-19 DE-BY-UBM DE-12 DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-824 DE-29T DE-19 DE-BY-UBM DE-12 DE-706 DE-83 DE-188 |
| physical | XXIX, 776 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | North-Holland |
| record_format | marc |
| series | Studies in mathematics and its applications |
| series2 | Studies in mathematics and its applications |
| spelling | Glowinski, Roland 1937-2022 Verfasser (DE-588)120514737 aut Analyse numérique des inéquations variationnelles Numerical analysis of variational inequalities Roland Glowinski ; Jacques-Louis Lions ; Raymond Trémolières Amsterdam [u.a.] North-Holland 1981 XXIX, 776 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in mathematics and its applications 8 Analyse numérique Inégalités différentielles Differential inequalities Numerical analysis Variational inequalities (Mathematics) Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialungleichung (DE-588)4149785-5 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Differentialungleichung (DE-588)4149785-5 s Variationsungleichung (DE-588)4187420-1 s Lions, Jacques-Louis 1928-2001 Verfasser (DE-588)124055397 aut Trémolières, Raymond Verfasser aut Studies in mathematics and its applications 8 (DE-604)BV000000646 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001363612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Glowinski, Roland 1937-2022 Lions, Jacques-Louis 1928-2001 Trémolières, Raymond Numerical analysis of variational inequalities Studies in mathematics and its applications Analyse numérique Inégalités différentielles Differential inequalities Numerical analysis Variational inequalities (Mathematics) Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Differentialungleichung (DE-588)4149785-5 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4012249-9 (DE-588)4149785-5 (DE-588)4187420-1 |
| title | Numerical analysis of variational inequalities |
| title_alt | Analyse numérique des inéquations variationnelles |
| title_auth | Numerical analysis of variational inequalities |
| title_exact_search | Numerical analysis of variational inequalities |
| title_full | Numerical analysis of variational inequalities Roland Glowinski ; Jacques-Louis Lions ; Raymond Trémolières |
| title_fullStr | Numerical analysis of variational inequalities Roland Glowinski ; Jacques-Louis Lions ; Raymond Trémolières |
| title_full_unstemmed | Numerical analysis of variational inequalities Roland Glowinski ; Jacques-Louis Lions ; Raymond Trémolières |
| title_short | Numerical analysis of variational inequalities |
| title_sort | numerical analysis of variational inequalities |
| topic | Analyse numérique Inégalités différentielles Differential inequalities Numerical analysis Variational inequalities (Mathematics) Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Differentialungleichung (DE-588)4149785-5 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| topic_facet | Analyse numérique Inégalités différentielles Differential inequalities Numerical analysis Variational inequalities (Mathematics) Numerisches Verfahren Differentialgleichung Differentialungleichung Variationsungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001363612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000646 |
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