The least squares finite element method: theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Scientific computation
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. 399 - 412 |
| Beschreibung: | XVI, 418 S. graph. Darst. |
| ISBN: | 3540639349 |
Internformat
MARC
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| 100 | 1 | |a Jiang, Bo-Nan |d 1940- |e Verfasser |0 (DE-588)118011766 |4 aut | |
| 245 | 1 | 0 | |a The least squares finite element method |b theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables |c Bo-nan Jiang |
| 246 | 1 | |a The least-squares finite element method | |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XVI, 418 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Scientific computation | |
| 500 | |a Literaturverz. 399 - 412 | ||
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Datensatz im Suchindex
| _version_ | 1804126265865666560 |
|---|---|
| adam_text | Contents
Part I. Basic Concepts of LSFEM
1. Introduction 3
1.1 Why Finite Elements? 3
1.2 Why Least Squares? 4
2. First Order Scalar Equation in One Dimension 11
2.1 A Model Problem 11
2.2 Function Spaces Hm(O) 12
2.3 The Classic Galerkin Method Global Approximation 14
2.4 The Least Squares Method Global Approximation 16
2.5 One Dimensional Finite Elements 18
2.6 The Classic Galerkin Finite Element Method 20
2.7 The Least Squares Finite Element Method 23
2.7.1 The Least Squares Formulation 23
2.7.2 The Euler Lagrange Equation 24
2.7.3 Error Estimates 26
2.7.4 Condition Number 28
2.7.5 A Numerical Example 29
2.8 Concluding Remarks 30
3. First Order System in One Dimension 31
3.1 A Model Problem 31
3.2 The Rayleigh Ritz Method 32
3.3 The Mixed Galerkin Method 33
3.4 The Least Squares Finite Element Method 37
3.4.1 The Least Squares Formulation 37
3.4.2 Stability Estimate 39
3.4.3 Error Analysis 41
3.4.4 Numerical Results 42
3.5 Concluding Remarks 44
XII Contents
Part II. Fundamentals of LSFEM
4. Basis of LSFEM 47
4.1 Function Spaces 47
4.2 Linear Operators 50
4.3 The Bounded Inverse Theorem 51
4.4 The Friedrichs Inequality 53
4.5 The Poincare Inequality 55
4.6 Finite Element Spaces 56
4.6.1 Regularity Requirements 56
4.6.2 Linear Triangular Element 57
4.6.3 Interpolation Errors 59
4.7 First Order System 64
4.8 General Formulation of LSFEM 66
4.9 The Euler Lagrange Equation 69
4.10 Error Estimates for LSFEM 69
4.10.1 General Problems 69
4.10.2 Elliptic Problems 71
4.11 Implementation of LSFEM 72
4.11.1 The Least Squares Solution
to Linear Algebraic Equations 73
4.11.2 The Least Squares Finite Element Collocation Method 76
4.11.3 Importance of the Order of Gaussian Quadrature 77
4.12 Concluding Remarks 78
5. Div Curl System 81
5.1 Basic Theorems 81
5.2 Determinacy and Ellipticity 86
5.3 The Div Curl Method 88
5.4 The Least Squares Method 90
5.5 The Euler Lagrange Equation 91
5.6 The Friedrichs Second Div Curl Inequality 93
5.7 Concluding Remarks 95
6. Div Curl Grad System . 97
6.1 A Model Problem 97
6.2 The Mixed Galerkin Method 98
6.3 The Conventional LSFEM 100
6.4 The Optimal LSFEM 102
6.4.1 Two Dimensional Case 103
6.4.2 Three Dimensional Case 105
6.4.3 Error Analysis 108
6.5 Numerical Results 110
6.6 Concluding Remarks Ill
Contents XIII
Part III. LSFEM in Fluid Dynamics
7. Inviscid Irrotational Flows 115
7.1 Incompressible Irrotational Flow 115
7.2 Subsonic Compressible Irrotational Flow 119
7.2.1 The First Order Governing Equations 119
7.2.2 Application of LSFEM 122
7.2.3 Examples 125
7.3 Concluding Remarks 127
8. Incompressible Viscous Flows 129
8.1 The Stokes Equations in the u—p Formulation 130
8.1.1 The Mixed Galerkin Method 130
8.1.2 The Mixed Galerkin/Least Squares Method 131
8.2 The Stokes Equations in the u—p — u Formulation 132
8.2.1 Determinacy and Ellipticity 133
8.2.2 Boundary Conditions 135
8.2.3 Application of LSFEM 143
8.3 The Navier Stokes Equations in the u — p — U) Formulation .. 146
8.3.1 Two Dimensional Case 149
8.3.2 Axisymmetric Case 152
8.3.3 Three Dimensional Case 153
8.4 The Navier Stokes Equations in the u — b — us Formulation .. 167
8.5 The Navier Stokes Equations in the u p a Formulation .. 168
8.6 Time Dependent Problems in the u p w Formulation 170
8.7 Fluid Thermal Coupling 175
8.7.1 Natural Convection 176
8.7.2 Rayleigh Benard Convection 177
8.7.3 Surface Tension Driven Convection 183
8.7.4 Double Diffusive Convection 188
8.8 The Second Order u — oj Formulation 191
8.8.1 The Stokes Equations 192
8.8.2 The Navier Stokes Equations 194
8.9 Concluding Remarks 197
9. Convective Transport 201
9.1 Steady State Problems 202
9.1.1 The Classic Galerkin Method 204
9.1.2 The SUPG Method 205
9.1.3 The Least Squares Finite Element Method 206
9.2 Contact Discontinuity 208
9.2.1 Introduction 208
9.2.2 The L Solution to Linear Algebraic Equations 209
9.2.3 The L Finite Element Method 213
XIV Contents
9.2.4 The Iteratively Reweighted LSFEM 218
9.2.5 Numerical Results of IRLSFEM 219
9.3 Transient Problems 225
9.3.1 The Taylor Galerkin Method 225
9.3.2 The Least Squares Finite Element Method 227
9.3.3 Numerical Examples of LSFEM 232
9.4 Concluding Remarks 239
10. Incompressible Inviscid Rotational Flows 241
10.1 Incompressible Euler Equations 242
10.1.1 The Velocity Pressure Formulation 242
10.1.2 The Velocity Pressure Vorticity Formulation 243
10.2 Energy Conservation 246
10.3 The Least Squares Finite Element Method 246
10.4 Numerical Results of LSFEM 249
10.5 Concluding Remarks 257
11. Low Speed Compressible Viscous Flows 259
11.1 Introduction 259
11.2 Two Dimensional Case 260
11.2.1 The Compressible Navier Stokes Equations 260
11.2.2 The First Order System for Low Speed Flows 264
11.2.3 The Div Curl Grad Formulation 265
11.2.4 The Least Squares Finite Element Method 268
11.2.5 Numerical Results 269
11.3 Three Dimensional Case 275
11.3.1 The Compressible Navier Stokes Equations 275
11.3.2 The Div Curl Grad Formulation 277
11.3.3 Numerical Results 278
11.4 Concluding Remarks 284
12. Two Fluid Flows 285
12.1 Introduction 285
12.2 Continuum Surface Force Model 287
12.3 The First Order Governing Equations 289
12.3.1 Rectangular Coordinates 289
12.3.2 Cylindrical Coordinates 291
12.4 Numerical Examples 293
12.5 Concluding Remarks 302
13. High Speed Compressible Flows 303
13.1 Various Least Squares Schemes 303
13.1.1 Non conservative £2 Scheme 303
13.1.2 Non conservative H1 Scheme 306
13.1.3 Conservative Schemes 308
Contents XV
13.2 One Dimensional Flows 310
13.3 Two Dimensional Flows 314
13.3.1 Non conservative Li Scheme 314
13.3.2 Conservative Scheme 321
13.4 Concluding Remarks 327
Part IV. LSFEM in Electromagnetics
14. Electromagnetics 331
14.1 The First Order Maxwell Equations 332
14.1.1 Basic Equations 333
14.1.2 Determinacy 334
14.1.3 Importance of Divergence Equations 337
14.2 The Second Order Maxwell Equations 338
14.2.1 The Div Curl Method 340
14.2.2 The Galerkin Method 343
14.2.3 The Least Squares Look Alike Method 345
14.2.4 Anisotropic Media 347
14.3 Electrostatic Fields 349
14.3.1 Electric Potential 350
14.3.2 The Least Squares Finite Element Method 350
14.4 Magnetostatic Fields 355
14.4.1 Magnetostatic Vector Potential 356
14.4.2 The Least Squares Finite Element Method 357
14.5 Time Harmonic Fields 358
14.5.1 Three Dimensional Time Harmonic Waves 358
14.5.2 Time Harmonic TE Waves 360
14.6 Transient Scattering Waves 364
14.6.1 TM and TE Waves 367
14.6.2 Time Discretization 369
14.6.3 Numerical Examples 371
14.6.4 Influence of Divergence Equations 379
14.7 Conclusion Remarks 381
Part V. Solution of Discrete Equations
15. The Element by Element Conjugate Gradient Method .... 385
15.1 Element by Element Technique 385
15.2 Matrix Free Algorithm 387
15.3 The Conjugate Gradient Method 388
15.3.1 The Steepest Descent Method 388
15.3.2 The Conjugate Gradient Method 390
15.3.3 The Preconditioned Conjugate Gradient Method 392
XVI Contents
15.3.4 Numerical Results and Comparisons 393
15.4 Concluding Remarks 395
Appendices 397
A. Operations on Vectors 397
B. Green s Formula 397
C. Poincare Inequality 398
D. Lax Milgram Theorem 398
References 399
Index 413
|
| any_adam_object | 1 |
| author | Jiang, Bo-Nan 1940- |
| author_GND | (DE-588)118011766 |
| author_facet | Jiang, Bo-Nan 1940- |
| author_role | aut |
| author_sort | Jiang, Bo-Nan 1940- |
| author_variant | b n j bnj |
| building | Verbundindex |
| bvnumber | BV011725911 |
| classification_rvk | SK 910 |
| classification_tum | MAT 674f PHY 220f PHY 302f |
| ctrlnum | (OCoLC)845035476 (DE-599)BVBBV011725911 |
| dewey-full | 532.05101515353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.05101515353 |
| dewey-search | 532.05101515353 |
| dewey-sort | 3532.05101515353 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV011725911 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:14:43Z |
| institution | BVB |
| isbn | 3540639349 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007909092 |
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| physical | XVI, 418 S. graph. Darst. |
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| publisher | Springer |
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| series2 | Scientific computation |
| spelling | Jiang, Bo-Nan 1940- Verfasser (DE-588)118011766 aut The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables Bo-nan Jiang The least-squares finite element method Berlin [u.a.] Springer 1998 XVI, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Scientific computation Literaturverz. 399 - 412 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Elektromagnetismus (DE-588)4014306-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Finite-Elemente-Methode (DE-588)4017233-8 s Methode der kleinsten Quadrate (DE-588)4038974-1 s DE-604 Strömungsmechanik (DE-588)4077970-1 s 1\p DE-604 Elektromagnetismus (DE-588)4014306-5 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jiang, Bo-Nan 1940- The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables Partielle Differentialgleichung (DE-588)4044779-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Elektromagnetismus (DE-588)4014306-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4077970-1 (DE-588)4017233-8 (DE-588)4038974-1 (DE-588)4014306-5 |
| title | The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables |
| title_alt | The least-squares finite element method |
| title_auth | The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables |
| title_exact_search | The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables |
| title_full | The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables Bo-nan Jiang |
| title_fullStr | The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables Bo-nan Jiang |
| title_full_unstemmed | The least squares finite element method theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables Bo-nan Jiang |
| title_short | The least squares finite element method |
| title_sort | the least squares finite element method theory and applications in computational fluid dynamics and electromagnetics with 11 tables |
| title_sub | theory and applications in computational fluid dynamics and electromagnetics ; with 11 tables |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Elektromagnetismus (DE-588)4014306-5 gnd |
| topic_facet | Partielle Differentialgleichung Strömungsmechanik Finite-Elemente-Methode Methode der kleinsten Quadrate Elektromagnetismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jiangbonan theleastsquaresfiniteelementmethodtheoryandapplicationsincomputationalfluiddynamicsandelectromagneticswith11tables AT jiangbonan theleastsquaresfiniteelementmethod |