Numerical approximation methods for elliptic boundary value problems: finite and boundary elements
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 386 S. graph. Darst. |
| ISBN: | 9780387313122 |
Internformat
MARC
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| 020 | |a 9780387313122 |9 978-0-387-31312-2 | ||
| 035 | |a (OCoLC)77256546 | ||
| 035 | |a (DE-599)BVBBV021996531 | ||
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| 100 | 1 | |a Steinbach, Olaf |d 1967- |e Verfasser |0 (DE-588)128588756 |4 aut | |
| 240 | 1 | 0 | |a Numerische Näherungsverfahren für elliptische Randwertprobleme |
| 245 | 1 | 0 | |a Numerical approximation methods for elliptic boundary value problems |b finite and boundary elements |c Olaf Steinbach |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XII, 386 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Boundary element methods | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Finite element method | |
| 650 | 0 | 7 | |a Randelemente-Methode |0 (DE-588)4076508-8 |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 Elliptisches Randwertproblem |0 (DE-588)4193399-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |D s |
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Datensatz im Suchindex
| _version_ | 1804135971486171136 |
|---|---|
| adam_text | Contents
1
Boundary Value Problems
................................. 1
1.1
Potential Equation
...................................... 1
1.2
Linear Elasticity
........................................ 5
1.2.1
Plane Elasticity
................................... 9
1.2.2
Incompressible Elasticity
........................... 12
1.3
Stokes System
.......................................... 12
1.4
Helmholtz Equation
..................................... 15
1.5
Exercises
............................................... 17
2
Function Spaces
........................................... 19
2.1
The Spaces
Ск(П), Ск^(П)
and
Lp{ü) .................... 19
2.2
Generalized Derivatives and Sobolev Spaces
................. 22
2.3
Properties of Sobolev Spaces
.............................. 25
2.4
Distributions and Sobolev Spaces
.......................... 29
2.5
Sobolev Spaces on Manifolds
.............................. 35
2.6
Exercises
............................................... 39
3
Variational Methods
....................................... 41
3.1
Operator Equations
...................................... 41
3.2
Elliptic Operators
....................................... 46
3.3
Operators and Stability Conditions
........................ 48
3.4
Operator Equations with Constraints
...................... 50
3.5
Mixed Formulations
..................................... 52
3.6
Coercive Operators
...................................... 57
4
Variational Formulations of Boundary Value Problems
..... 59
4.1
Potential Equation
...................................... 59
4.1.1
Dirichlet Boundary Value Problem
.................. 61
4.1.2
Lagrange Multiplier Methods
....................... 64
4.1.3
Neumann Boundary Value Problem
.................. 67
4.1.4
Mixed Boundary Value Problem
..................... 70
X
Contents
4.1.5
Robin Boundary Value Problems
.................... 71
4.2
Linear Elasticity
........................................ 72
4.2.1
Dirichlet Boundary Value Problem
.................. 76
4.2.2
Neumann Boundary Value Problem
.................. 77
4.2.3
Mixed Boundary Value Problems
.................... 79
4.3
Stokes Problem
......................................... 79
4.4
Helmholtz Equation
..................................... 85
4.5
Exercises
............................................... 86
5
Fundamental Solutions
.................................... 89
5.1
Laplace Operator
........................................ 90
5.2
Linear Elasticity
........................................ 96
5.3
Stokes Problem
.........................................101
5.4
Hehuholtz Equation
.....................................105
5.5
Exercises
...............................................109
6
Boundary Integral Operators
..............................
Ill
6.1
Newton Potential
........................................
Ill
6.2
Single Layer Potential
....................................118
6.3
Adjoint Double Layer Potential
...........................120
6.4
Double Layer Potential
...................................124
6.5
Hypcrsingular Boundary Integral Operator
.................128
6.6
Properties of Boundary Integral Operators
..................136
6.6.1
Ellipticity of the Single Layer Potential
..............139
6.6.2
Ellipticity of the Hypersingular Boundary Integral
Operator
.........................................144
6.6.3
Steklov
-Poincaré
Operator
.........................148
6.6.4
Contraction Estimates of the Double Layer Potential.
.. 149
6.6.5
Mapping Properties
................................152
6.7
Linear Elasticity
........................................155
6.8
Stokes System
..........................................165
6.9
Helmholtz Equation
.....................................167
6.10
Exercises
...............................................169
7
Boundary Integral Equations
..............................171
7.1
Dirichlet Boundary Value Problem
.........................172
7.2
Neumann Boundary Value Problem
........................175
7.3
Mixed Boundary Conditions
..............................179
7.4
Robin Boundary Conditions
..............................181
7.5
Exterior Boundary Value Problems
........................181
7.6
Helmholtz Equation
.....................................183
7.7
Exercises
...............................................
igQ
Contents
XI
8 Approximation
Methods...................................
187
8.1 Galerkin-Bubnov
Methods ...............................
187
8.2 Approximation
of the
Linear Form.........................190
8.3 Approximation
of the
Operator ...........................191
8.4 Galerkin-Petrov
Methods
................................193
8.5
Mixed Formulations
.....................................195
8.6
Coercive Operators
......................................199
8.7
Exercises
...............................................202
9
Finite Elements
............................................203
9.1
Reference Elements
......................................203
9.2
Form Functions
.........................................211
9.3
Trial Spaces
............................................216
9.4
Quasi Interpolation Operators
.............................225
9.5
Exercises
...............................................227
10
Boundary Elements
........................................229
10.1
Reference Elements
......................................229
10.2
Trial Spaces
............................................233
11
Finite Element Methods
...................................243
11.1
Dirichlet Boundary Value Problem
.........................243
11.2
Neumann Boundary Value Problem
........................253
11.3
Finite Element Methods with
Lagrange
Multipliers
..........255
11.4
Exercises
...............................................261
12
Boundary Element Methods
...............................263
12.1
Dirichlet Boundary Value Problem
.........................263
12.2
Neumann Boundary Value Problem
........................274
12.3
Mixed Boundary Conditions
..............................281
12.4
Robin Boundary Conditions
..............................287
12.5
Exercises
...............................................289
13
Iterative Solution Methods
................................291
13.1
The Method of Conjugate Gradients
.......................291
13.2
A General Preconditioning Strategy
.......................299
13.2.1
An Application in Boundary Element Alethods
........302
13.2.2
A Multilevel Preconditioner
in Finite Element Methods
.........................306
13.3
Solution Methods for Saddle Point Problems
................319
14
Fast Boundary Element Methods
..........................327
14.1
Hierarchical Cluster Methods
.............................328
14.2
Approximation of the Stiffness Matrix
......................332
14.2.1
Taylor Series Representations
.......................336
14.2.2
Series Representations of the Fundamental Solution
.... 340
14.2.3
Adaptive Cross Approximation
......................344
XII Contents
14.3
Wavelets
...............................................351
14.4
Exercises
...............................................366
15
Domain Decomposition Methods
..........................367
References
.....................................................375
Index
..........................................................383
|
| adam_txt |
Contents
1
Boundary Value Problems
. 1
1.1
Potential Equation
. 1
1.2
Linear Elasticity
. 5
1.2.1
Plane Elasticity
. 9
1.2.2
Incompressible Elasticity
. 12
1.3
Stokes System
. 12
1.4
Helmholtz Equation
. 15
1.5
Exercises
. 17
2
Function Spaces
. 19
2.1
The Spaces
Ск(П), Ск^(П)
and
Lp{ü) . 19
2.2
Generalized Derivatives and Sobolev Spaces
. 22
2.3
Properties of Sobolev Spaces
. 25
2.4
Distributions and Sobolev Spaces
. 29
2.5
Sobolev Spaces on Manifolds
. 35
2.6
Exercises
. 39
3
Variational Methods
. 41
3.1
Operator Equations
. 41
3.2
Elliptic Operators
. 46
3.3
Operators and Stability Conditions
. 48
3.4
Operator Equations with Constraints
. 50
3.5
Mixed Formulations
. 52
3.6
Coercive Operators
. 57
4
Variational Formulations of Boundary Value Problems
. 59
4.1
Potential Equation
. 59
4.1.1
Dirichlet Boundary Value Problem
. 61
4.1.2
Lagrange Multiplier Methods
. 64
4.1.3
Neumann Boundary Value Problem
. 67
4.1.4
Mixed Boundary Value Problem
. 70
X
Contents
4.1.5
Robin Boundary Value Problems
. 71
4.2
Linear Elasticity
. 72
4.2.1
Dirichlet Boundary Value Problem
. 76
4.2.2
Neumann Boundary Value Problem
. 77
4.2.3
Mixed Boundary Value Problems
. 79
4.3
Stokes Problem
. 79
4.4
Helmholtz Equation
. 85
4.5
Exercises
. 86
5
Fundamental Solutions
. 89
5.1
Laplace Operator
. 90
5.2
Linear Elasticity
. 96
5.3
Stokes Problem
.101
5.4
Hehuholtz Equation
.105
5.5
Exercises
.109
6
Boundary Integral Operators
.
Ill
6.1
Newton Potential
.
Ill
6.2
Single Layer Potential
.118
6.3
Adjoint Double Layer Potential
.120
6.4
Double Layer Potential
.124
6.5
Hypcrsingular Boundary Integral Operator
.128
6.6
Properties of Boundary Integral Operators
.136
6.6.1
Ellipticity of the Single Layer Potential
.139
6.6.2
Ellipticity of the Hypersingular Boundary Integral
Operator
.144
6.6.3
Steklov
-Poincaré
Operator
.148
6.6.4
Contraction Estimates of the Double Layer Potential.
. 149
6.6.5
Mapping Properties
.152
6.7
Linear Elasticity
.155
6.8
Stokes System
.165
6.9
Helmholtz Equation
.167
6.10
Exercises
.169
7
Boundary Integral Equations
.171
7.1
Dirichlet Boundary Value Problem
.172
7.2
Neumann Boundary Value Problem
.175
7.3
Mixed Boundary Conditions
.179
7.4
Robin Boundary Conditions
.181
7.5
Exterior Boundary Value Problems
.181
7.6
Helmholtz Equation
.183
7.7
Exercises
.
igQ
Contents
XI
8 Approximation
Methods.
187
8.1 Galerkin-Bubnov
Methods .
187
8.2 Approximation
of the
Linear Form.190
8.3 Approximation
of the
Operator .191
8.4 Galerkin-Petrov
Methods
.193
8.5
Mixed Formulations
.195
8.6
Coercive Operators
.199
8.7
Exercises
.202
9
Finite Elements
.203
9.1
Reference Elements
.203
9.2
Form Functions
.211
9.3
Trial Spaces
.216
9.4
Quasi Interpolation Operators
.225
9.5
Exercises
.227
10
Boundary Elements
.229
10.1
Reference Elements
.229
10.2
Trial Spaces
.233
11
Finite Element Methods
.243
11.1
Dirichlet Boundary Value Problem
.243
11.2
Neumann Boundary Value Problem
.253
11.3
Finite Element Methods with
Lagrange
Multipliers
.255
11.4
Exercises
.261
12
Boundary Element Methods
.263
12.1
Dirichlet Boundary Value Problem
.263
12.2
Neumann Boundary Value Problem
.274
12.3
Mixed Boundary Conditions
.281
12.4
Robin Boundary Conditions
.287
12.5
Exercises
.289
13
Iterative Solution Methods
.291
13.1
The Method of Conjugate Gradients
.291
13.2
A General Preconditioning Strategy
.299
13.2.1
An Application in Boundary Element Alethods
.302
13.2.2
A Multilevel Preconditioner
in Finite Element Methods
.306
13.3
Solution Methods for Saddle Point Problems
.319
14
Fast Boundary Element Methods
.327
14.1
Hierarchical Cluster Methods
.328
14.2
Approximation of the Stiffness Matrix
.332
14.2.1
Taylor Series Representations
.336
14.2.2
Series Representations of the Fundamental Solution
. 340
14.2.3
Adaptive Cross Approximation
.344
XII Contents
14.3
Wavelets
.351
14.4
Exercises
.366
15
Domain Decomposition Methods
.367
References
.375
Index
.383 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Steinbach, Olaf 1967- |
| author_GND | (DE-588)128588756 |
| author_facet | Steinbach, Olaf 1967- |
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| callnumber-label | QA379 |
| callnumber-raw | QA379 |
| callnumber-search | QA379 |
| callnumber-sort | QA 3379 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 910 SK 920 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)77256546 (DE-599)BVBBV021996531 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV021996531 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:10:52Z |
| indexdate | 2024-07-09T20:48:59Z |
| institution | BVB |
| isbn | 9780387313122 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015211208 |
| oclc_num | 77256546 |
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| physical | XII, 386 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | Springer |
| record_format | marc |
| spelling | Steinbach, Olaf 1967- Verfasser (DE-588)128588756 aut Numerische Näherungsverfahren für elliptische Randwertprobleme Numerical approximation methods for elliptic boundary value problems finite and boundary elements Olaf Steinbach New York, NY Springer 2008 XII, 386 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Boundary element methods Boundary value problems Numerical solutions Finite element method Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Elliptisches Randwertproblem (DE-588)4193399-0 s Finite-Elemente-Methode (DE-588)4017233-8 s Randelemente-Methode (DE-588)4076508-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015211208&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steinbach, Olaf 1967- Numerical approximation methods for elliptic boundary value problems finite and boundary elements Boundary element methods Boundary value problems Numerical solutions Finite element method Randelemente-Methode (DE-588)4076508-8 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4076508-8 (DE-588)4017233-8 (DE-588)4193399-0 (DE-588)4123623-3 |
| title | Numerical approximation methods for elliptic boundary value problems finite and boundary elements |
| title_alt | Numerische Näherungsverfahren für elliptische Randwertprobleme |
| title_auth | Numerical approximation methods for elliptic boundary value problems finite and boundary elements |
| title_exact_search | Numerical approximation methods for elliptic boundary value problems finite and boundary elements |
| title_exact_search_txtP | Numerical approximation methods for elliptic boundary value problems finite and boundary elements |
| title_full | Numerical approximation methods for elliptic boundary value problems finite and boundary elements Olaf Steinbach |
| title_fullStr | Numerical approximation methods for elliptic boundary value problems finite and boundary elements Olaf Steinbach |
| title_full_unstemmed | Numerical approximation methods for elliptic boundary value problems finite and boundary elements Olaf Steinbach |
| title_short | Numerical approximation methods for elliptic boundary value problems |
| title_sort | numerical approximation methods for elliptic boundary value problems finite and boundary elements |
| title_sub | finite and boundary elements |
| topic | Boundary element methods Boundary value problems Numerical solutions Finite element method Randelemente-Methode (DE-588)4076508-8 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Boundary element methods Boundary value problems Numerical solutions Finite element method Randelemente-Methode Finite-Elemente-Methode Elliptisches Randwertproblem Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015211208&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT steinbacholaf numerischenaherungsverfahrenfurelliptischerandwertprobleme AT steinbacholaf numericalapproximationmethodsforellipticboundaryvalueproblemsfiniteandboundaryelements |