Finite element analysis and applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Wiley
1985
|
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 260 S. graph. Darst. |
| ISBN: | 0471906778 0471906786 |
Internformat
MARC
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| 001 | BV002290284 | ||
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| 007 | t | ||
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| 020 | |a 0471906786 |9 0-471-90678-6 | ||
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| 100 | 1 | |a Wait, R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Finite element analysis and applications |c R. Wait ; A. R. Mitchell |
| 264 | 1 | |a Chichester u.a. |b Wiley |c 1985 | |
| 300 | |a XII, 260 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a A Wiley-Interscience publication | |
| 650 | 4 | |a Éléments finis, Méthode des | |
| 650 | 4 | |a Finite element method | |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Mitchell, Andrew R. |d 1921- |e Verfasser |0 (DE-588)120016885 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001505013 | ||
Datensatz im Suchindex
| _version_ | 1804116749901103104 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Approximation by piecewise polynomials 1
1.1.1 Bivariate approximation 8
1.2 Function spaces 12
1.2.1 Hilbert spaces 13
1.2.2 Linear operators 14
1.2.3 Approximating subspaces 20
1.2.4 Sobolev spaces 23
1.2.5 Green s theorem 25
2 Variational principles 27
2.1 Introduction 27
2.2 Stable equilibrium problems 29
2.3 Boundary conditions 32
2.4 Time dependent variational principles 35
2.5 Dual variational principles 37
3 Basis functions 41
3.1 The triangle 41
3.1.1 Lagrange interpolation 41
3.1.2 The standard triangle 44
3.1.3 Hermite interpolation 46
3.1.4 C1 approximating functions 49
3.2 The rectangle 51
3.2.1 Lagrange interpolation 51
3.2.2 Bicubic Hermite interpolation 53
3.2.3 The quadrilateral 55
3.3 Curved boundaries 57
3.3.1 Direct methods: triangle with one curved side 57
3.3.2 Isoparametric transformations 60
3.3.3 The unit square reference element 60
3.3.4 The hexahedron 62
ix
x Contents
3.3.5 The quadratic triangle 64
3.3.6 Cubic approximation 68
3.3.7 High order bases 70
3.4 Nonconforming elements 72
4 Methods of approximation 73
4.1 Introduction 73
4.1.1 Ritz methods 74
4.2 Galerkin methods 76
4.2.1 Weak solutions 76
4.2.2 Numerical example 1 82
4.2.3 Numerical example 2 88
4.2.4 Nonconforming methods 92
4.2.5 Higher order elements 98
4.2.6 Penalty methods: numerical example 3 99
4.3 Petrov Galerkin methods 101
4.3.1 Upwinding 102
4.3.2 Nonphysical models 112
4.3.3 Method of collocation 113
4.3.4 Collocation Galerkin method 115
4.3.5 Spline collocation 117
4.3.6 H~l and H1 Galerkin methods 120
4.4 Nonlinear equations and systems 121
4.4.1 Numerical example 4 125
4.4.2 Systems of equations 127
4.4.3 Numerical example 5: plane stress 128
4.4.4 The biharmonic equation 131
4.5 Computational considerations 132
4.5.1 Constructing element matrices 133
4.5.2 Solving global equations 134
4.5.3 Alternating direction Galerkin methods for rectangular
regions 135
4.5.4 Conjugate gradients 139
5 Time dependent problems 140
5.1 Hamilton s principle 140
5.1.1 Dissipative systems 144
5.2 Semi discrete Galerkin methods 146
5.2.1 Introduction 146
5.2.2 Simple example 149
5.2.3 Hyperbolic equations 150
5.2.4 Nonlinear problems 151
Contents xi
5.3 Discretization in time 153
5.3.1 Finite difference methods 153
5.3.2 Numerical example 156
5.3.3 Stability of time discretizations 159
5.3.4 Numerical stability of the CNG method 164
5.3.5 One step Galerkin methods: finite elements in time ... 167
5.3.6 ADG methods for parabolic equations 169
6 Convergence of approximation 170
6.1 Introduction 170
6.1.1 The Bramble Hilbert lemma 171
6.1.2 Regular transformations 175
6.1.3 Complete approximations 179
6.2 Convergence of Galerkin approximations 181
6.2.1 Energy bounds 181
6.2.2 Alternative norms 184
6.2.3 Boundary approximation and quadrature 186
6.3 Approximation errors 187
6.3.1 Interpolation error bounds and Galerkin error bounds . . 188
6.3.2 Curved elements 191
6.3.3 gm error bounds 194
6.4 Perturbation errors 196
6.4.1 Numerical integration 196
6.4.2 Interpolated boundary conditions 201
6.4.3 Boundary approximation 203
6.4.4 Penalty methods 205
6.4.5 Nonconforming elements 206
6.5 Convergence of semi discrete Galerkin approximations.... 212
7 Developments and applications •¦ 215
7.1 Introduction: product approximation 215
7.2 Reaction diffusion 216
7.2.1 Fisher s equation (m = n = 1) 217
7.2.2 The Fitzhugh Nagumo (FN) system 220
7.3 Solitons 225
7.3.1 The KdV equation 225
7.3.2 The Sine Gordon equation 229
7.4 Conduction convection 230
7.4.1 Time dependent problems 231
7.4.2 The nonlinear case: Burger s equation 232
7.5 Singular isoparametric elements 234
xii Contents
7.6 First order hyperbolic equations 239
7.6.1 Stability and phase error 241
7.7 The moving finite element method 248
7.7.1 Equidistributing principles 250
References 252
Index 258
|
| any_adam_object | 1 |
| author | Wait, R. Mitchell, Andrew R. 1921- |
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| author_facet | Wait, R. Mitchell, Andrew R. 1921- |
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| callnumber-first | T - Technology |
| callnumber-label | TA347 |
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| callnumber-search | TA347.F5 |
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| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 910 SK 920 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)11469726 (DE-599)BVBBV002290284 |
| dewey-full | 620/.001/515353 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620/.001/515353 |
| dewey-search | 620/.001/515353 |
| dewey-sort | 3620 11 6515353 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002290284 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:28Z |
| institution | BVB |
| isbn | 0471906778 0471906786 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001505013 |
| oclc_num | 11469726 |
| open_access_boolean | |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-703 DE-29T DE-706 DE-188 |
| physical | XII, 260 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley-Interscience publication |
| spelling | Wait, R. Verfasser aut Finite element analysis and applications R. Wait ; A. R. Mitchell Chichester u.a. Wiley 1985 XII, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Éléments finis, Méthode des Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Mitchell, Andrew R. 1921- Verfasser (DE-588)120016885 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wait, R. Mitchell, Andrew R. 1921- Finite element analysis and applications Éléments finis, Méthode des Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | Finite element analysis and applications |
| title_auth | Finite element analysis and applications |
| title_exact_search | Finite element analysis and applications |
| title_full | Finite element analysis and applications R. Wait ; A. R. Mitchell |
| title_fullStr | Finite element analysis and applications R. Wait ; A. R. Mitchell |
| title_full_unstemmed | Finite element analysis and applications R. Wait ; A. R. Mitchell |
| title_short | Finite element analysis and applications |
| title_sort | finite element analysis and applications |
| topic | Éléments finis, Méthode des Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Éléments finis, Méthode des Finite element method Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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