Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2014
|
| Edition: | 2. ed. |
| Series: | Numerical mathematics and scientific computation
Oxford science publications |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 479 S. graph. Darst. |
| ISBN: | 9780199678792 9780199678808 |
Staff View
MARC
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| 245 | 1 | 0 | |a Finite elements and fast iterative solvers |b with applications in incompressible fluid dynamics |c Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2014 | |
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| 650 | 7 | |a Método dos elementos finitos |2 larpcal | |
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| 650 | 4 | |a Finite element method | |
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Record in the Search Index
| _version_ | 1804152173952499712 |
|---|---|
| adam_text | CONTENTS
Models of incompressible fluid flow
1
The
Poisson
equation
9
1.1
Reference problems
10
1.2
Weak formulation
12
1.3
The Galerkin finite element method
16
1.3.1
Triangular elements (R2)
18
1.3.2
Quadrilateral elements (R2)
21
1.3.3
Tetrahedral elements (R3)
23
1.3.4
Brick elements (R3)
24
1.4
Implementation aspects
25
1.4.1
Triangular element matrices
2(3
1.4.2
Quadrilateral element matrices
2
У
1.4.3
Assembly of the Galerkin system
31
1.5
Theory of errors
34
1.5.1
A priori error bounds
36
1.5.2
A posteriori error bounds
47
1.6
Matrix
proporties
54
Problems
59
Computational exercises
67
Solution of discrete
Poisson
problems
70
2.1
The conjugate gradient method
71
2.1.1
Convergence analysis
75
2.1.2
Stopping criteria
77
2.2
Preconditioning
80
2.2.1
General principles of preconditioning
80
2.2.2
Stationary iteration
85
2.3
Singular systems are not a problem
86
2.4
The Lanczos and minimum
residuai
methods
87
2.5
Multigrid
91
2.5.1
Two-grid convergence theory
98
2.5.2
Extending two-grid to multigrid
104
2.5.3
Algebraic multigrid
110
Problems
112
Computational exercises
116
The Stokes equations
119
3.1
Reference problems
122
3.2
Weak formulation
126
XI
xii CONTENTS
3.3 Approximation
using mixed finite elements
129
3.3.1
Stable rectangular elements (C^^Qi, Q2—P-1,
Q2-P0)
133
3.3.2
Stabilized rectangular elements (Qi-Pq, Q -Q )
139
3.3.3
Triangular elements
149
3-3.4
Brick and tetrahedral elements
152
3.4
Theory of errors
153
3.4.1
A priori error bounds
154
3.4.2
A posteriori error bounds
166
3.5
Matrix properties
171
3.5.1
Stable mixed approximation
174
3.5.2
Stabilized mixed approximation
177
Discussion and bibliographical notes
181
Problems
184
Computational exercises
186
4
Solution of discrete Stokes problems
189
4.1
The preconditioned MINRES method
190
4.2
Preconditioning
193
4.2.1
General strategies for preconditioning
194
4.2.2
Eigenvalue bounds
200
4.2.3
Equivalent norms for MINRES
207
4.2.4
MINRES convergence analysis
210
Discussion and bibliographical notes
212
Problems
213
Computational exercises
215
б
Optimization with PDE constraints
217
5.1
Reference problems
218
5.2
Optimization, discretization
221
5.3
Preconditioning
225
Discussion and bibliographical notes
230
Problems
230
Computational exercises
232
6
The convection-diffusion equation
234
6.1
Reference problems
236
6.2
Weak formulation and the convection term
241
6.3
Approximation by finite elements
244
6.3.1
The Galerkin finite element method
244
6.3.2
The streamline diffusion method
247
6.4
Theory of errors
255
6.4.1
A priori error bounds
255
6.4.2
A posteriori error bounds
262
6.5
Matrix properties
269
CONTENTS xiii
6.5.1
Computational molecules and Fourier analysis
272
6.5.2
Analysis of difference equations
276
Discussion and bibliographical notes
281
Problems
283
Computational exercises
284
7
Solution of discrete convection—diffusion problems
286
7.1
Krylov subspace methods
286
7.1.1
GMRES
287
7.1.2
Biorthogonalization methods
292
7.2
Preconditioning methods and splitting operators
296
7.2.1
Splitting operators for convection-diffusion systems
298
7.2.2
Matrix analysis of convergence
301
7.2.3
Asymptotic analysis of convergence
305
7.2.4
Practical considerations
309
7.3
Multigrid
314
7.3.1
Practical considerations
315
7.3.2
Tools of analysis: smoothing and approximation
properties
319
7.3.3
Smoothing
321
7.3.4
Analysis
325
Discussion and bibliographical notes
327
Problems
330
Computational exercises
331
8
The
Navier—
Stokes equations
333
8.1
Reference problems
334
8.2
Weak formulation and linearization
338
8.2.1
Stability theory and bifurcation analysis
340
8.2.2
Nonlinear iteration
344
8.3
Mixed finite element approximation
346
8.4
Theory of errors
349
8.4.1
A priori error bounds
350
8.4.2
A posteriori error bounds
352
Discussion and bibliographical notes
356
Problems
357
Computational exercises
358
9
Solution of discrete
Navier—
Stokes problems
359
9.1
General strategies for preconditioning
360
9.2
Approximations to the
Schur
complement operator
364
9.2.1
The pressure convection-diffusion preconditioner
365
9.2.2
Boundary modifications for pressure
convection-diffusion preconditioning
371
9.2.3
The least-squares commutator preconditioner
376
xiv CONTENTS
9.2.4
Boundary modifications for the least-squares
commutator preconditioner
378
9.2.5
Adjustments of the least-squares commutator
for stabilized elements
380
9.3
Performance and analysis
384
9.3.1
Ideal versions of the preconditioners
385
9.3.2
impact of boundary conditions
389
9.3.3
Use of iterative methods for subproblems
390
9.3.4
Convergence analysis
394
9.3.5
Enclosed flow: singular systems are not a problem
395
9.3.6
Relation to SIMPLE iteration
398
9.4
Nonlinear iteration
400
Discussion and bibliographical notes
404
Problems
409
Computational exercises
410
10
Solution of unsteady
Navier—
Stokes equations
412
10.1
Reference problems
414
10.2
Weak formulation and implicit time stepping
419
10.2.1
Stability theory
422
10.2.2
Time-stepping algorithms
424
10.2.3
Adaptive time-step control and spatial approximation
429
10.3
Fast iterative solvers for the linearized systems
433
Discussion and bibliographical notes
436
Computational exercises
437
11
Solution of models of buoyancy-driven flow
439
11.1
Reference problems
442
11.2
Implicit time stepping
448
11.3
Fast iterative solvers for the linearized systems
451
Discussion and bibliographical notes
454
Computational exercises
454
References
457
Index
475
|
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| discipline | Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:06:31Z |
| institution | BVB |
| isbn | 9780199678792 9780199678808 |
| language | English |
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| series2 | Numerical mathematics and scientific computation Oxford science publications |
| spelling | Elman, Howard C. Verfasser (DE-588)141967862 aut Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen 2. ed. Oxford [u.a.] Oxford Univ. Press 2014 XIV, 479 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Oxford science publications Equações diferenciais parciais larpcal Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional larpcal Método dos elementos finitos larpcal Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Inkompressible Strömung (DE-588)4129759-3 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Partielle Differentialgleichung (DE-588)4044779-0 s Inkompressible Strömung (DE-588)4129759-3 s DE-604 Silvester, David J. Verfasser (DE-588)11391220X aut Wathen, Andrew J. Verfasser (DE-588)113912196 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027280017&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elman, Howard C. Silvester, David J. Wathen, Andrew J. Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Equações diferenciais parciais larpcal Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional larpcal Método dos elementos finitos larpcal Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Partielle Differentialgleichung (DE-588)4044779-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Inkompressible Strömung (DE-588)4129759-3 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4017233-8 (DE-588)4129759-3 |
| title | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_auth | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_exact_search | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_full | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| title_fullStr | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| title_full_unstemmed | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| title_short | Finite elements and fast iterative solvers |
| title_sort | finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_sub | with applications in incompressible fluid dynamics |
| topic | Equações diferenciais parciais larpcal Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional larpcal Método dos elementos finitos larpcal Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Partielle Differentialgleichung (DE-588)4044779-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Inkompressible Strömung (DE-588)4129759-3 gnd |
| topic_facet | Equações diferenciais parciais Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional Método dos elementos finitos Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Partielle Differentialgleichung Finite-Elemente-Methode Inkompressible Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027280017&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT elmanhowardc finiteelementsandfastiterativesolverswithapplicationsinincompressiblefluiddynamics AT silvesterdavidj finiteelementsandfastiterativesolverswithapplicationsinincompressiblefluiddynamics AT wathenandrewj finiteelementsandfastiterativesolverswithapplicationsinincompressiblefluiddynamics |