The finite element method: an introduction with partial differential equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | IX, 297 S. graph. Darst. |
| ISBN: | 9780199609130 0199609136 |
Internformat
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| 100 | 1 | |a Davies, Alan J. |e Verfasser |0 (DE-588)1015939368 |4 aut | |
| 245 | 1 | 0 | |a The finite element method |b an introduction with partial differential equations |c A. J . Davies |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a IX, 297 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804148445174300672 |
|---|---|
| adam_text | Contents
Historical introduction
1
Weighted residual and variational methods
7
2.1
Classification of differential operators
7
2.2
Self-adjoint positive definite operators
9
2.3
Weighted residual methods
12
2.4
Extrémům
formulation: homogeneous boundary
conditions
24
2.5
Non-homogeneous boundary conditions
28
2.6
Partial differential equations: natural boundary-
conditions
32
2.7
The Rayleigh-Ritz method
35
2.8
The elastic analogy for Poisson s equation
44
2.9
Variational methods for time-dependent problems
48
2.10
Exercises and solutions
50
The finite element method for elliptic problems
71
3.1
Difficulties associated with the application of weighted
residual methods
71
3.2
Piecewise application of the Galerkin method
72
3.3
Terminology
73
3.4
Finite element idealization
75
3.5
Illustrative problem involving one independent variable
80
3.6
Finite element equations for Poisson s equation
91
3.7
A rectangular element for Poisson s equation
102
3.8
A triangular element for Poisson s equation
107
3.9
Exercises and solutions
114
Higher-order elements: the isoparametric concept
141
4.1
A two-point boundary-value problem
141
4.2
Higher-order rectangular elements
144
4.3
Higher-order triangular elements
145
4.4
Two degrees of freedom at each node
147
4.5
Condensation of internal nodal freedoms
151
4.6
Curved boundaries and higher-order elements: isoparametric
elements
153
4.7
Exercises and solutions
160
viii The Finite Element
Method
5
Further topics in the finite element method
171
5.1
The variational approach
171
5.2
Collocation and least squares methods
177
5.3
Use of Galerkin s method for time-dependent and non-linear
problems
179
5.4
Time-dependent problems using variational principles which
are not extremal
189
5.5
The Laplace transform
192
5.6
Exercises and solutions
199
6
Convergence of the finite element method
218
6.1
A one-dimensional example
218
6.2
Two-dimensional problems involving Poisson s equation
224
6.3
Isoparametric elements: numerical integration
226
6.4
Non-conforming elements: the patch test
228
6.5
Comparison with the finite difference method: stability
229
6.6
Exercises and solutions
234
7
The boundary element method
244
7.1
Integral formulation of boundary-value problems
244
7.2
Boundary element idealization for Laplace s equation
247
7.3
A constant boundary element for Laplace s equation
251
7.4
A linear element for Laplace s equation
256
7.5
Time-dependent problems
259
7.6
Exercises and solutions
261
8
Computational aspects
270
8.1
Pre-processor
270
8.2
Solution phase
271
8.3
Post-processor
274
8.4
Finite element method
(FEM)
or boundary element method
(BEM)?
* 274
Appendix A Partial differential equation models in the physical
sciences
276
A.I Parabolic problems
276
A.2 Elliptic problems
277
A.3 Hyperbolic problems
278
A.
4
Initial and boundary conditions
279
Appendix
В
Some integral theorems of the vector calculus
280
Appendix
С
A formula for integrating products of area coordinates
over a triangle
282
Contents ix
Appendix
D
Numerical integration formulae
284
D.I One-dimensional Gauss quadrature
284
D.2 Two-dimensional Gauss quadrature
284
D.3 Logarithmic Gauss quadrature
285
Appendix
E
Stehfest s formula and weights for numerical Laplace
transform inversion
287
References
288
Index
295
The physical world around us can be described in mathematical terms. One way
to do so is with partial differential equations. The finite element method is a technique
for solving these equations which is particularly useful for more difficult problems such
as those involving surfaces with complicated geometry.
In the first instance, Davies develops the finite element method for the
solution of Poisson s equation. Time-dependent and non-linear problems are solved next.
The method is then extended to a weighted residual context and the relationship with
the variational approach is also explained. There are worked examples throughout and
each chapter has a set of exercises with detailed solutions.
Based on many years of experience of teaching the finite element
method to a varied audience, this book constitutes a major revision of the first
edition. It contains new chapters on the boundary element method and computational
methods, as well as a new section in the Appendix explaining the form of the partial
differential equations for a variety of practical applications. The careful, relatively
informal approach makes this suitable as an introductory text for undergraduate
mathematicians, engineers and physical scientists.
|
| any_adam_object | 1 |
| author | Davies, Alan J. |
| author_GND | (DE-588)1015939368 |
| author_facet | Davies, Alan J. |
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| author_sort | Davies, Alan J. |
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| building | Verbundindex |
| bvnumber | BV039604328 |
| classification_rvk | SK 910 SK 920 |
| classification_tum | MAT 355f MAT 674f |
| ctrlnum | (OCoLC)732847901 (DE-599)BVBBV039604328 |
| dewey-full | 518/.25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.25 |
| dewey-search | 518/.25 |
| dewey-sort | 3518 225 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:07:15Z |
| institution | BVB |
| isbn | 9780199609130 0199609136 |
| language | English |
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| spelling | Davies, Alan J. Verfasser (DE-588)1015939368 aut The finite element method an introduction with partial differential equations A. J . Davies 2. ed. Oxford [u.a.] Oxford Univ. Press 2011 IX, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024455128&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024455128&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Davies, Alan J. The finite element method an introduction with partial differential equations Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | The finite element method an introduction with partial differential equations |
| title_auth | The finite element method an introduction with partial differential equations |
| title_exact_search | The finite element method an introduction with partial differential equations |
| title_full | The finite element method an introduction with partial differential equations A. J . Davies |
| title_fullStr | The finite element method an introduction with partial differential equations A. J . Davies |
| title_full_unstemmed | The finite element method an introduction with partial differential equations A. J . Davies |
| title_short | The finite element method |
| title_sort | the finite element method an introduction with partial differential equations |
| title_sub | an introduction with partial differential equations |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite-Elemente-Methode |
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