The finite element method and its reliability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
2001
|
| Edition: | 1. publ. |
| Series: | Numerical mathematics and scientific computation
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 802 S. graph. Darst. |
| ISBN: | 0198502761 |
Staff View
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| 245 | 1 | 0 | |a The finite element method and its reliability |c Ivo Babuška and Theofanis Strouboulis |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 2001 | |
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Record in the Search Index
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| adam_text | CONTENTS
1 Introduction 1
1.0 Introduction 1
1.1 A brief history of the finite element method 2
1.2 On computational engineering 3
2 Mathematical formulation of the model problem 8
2.0 Introduction 8
2.1 The one dimensional model problem 8
2.1* The two dimensional model problem 13
2.2 The variational formulation of the model problem 19
2.2* The variational formulation of the model problem in two dimensions 37
2.3 Smoothness of the solution of the model problem 41
2.3* Smoothness of the solution of the two dimensional model problem 46
2.4 Historical and bibliographical remarks 49
3 The finite element method 52
3.0 Introduction 52
3.1 The Galerkin method and the properties of the approximate solution 54
3.1* The Galerkin method in two dimensions 64
3.2 The finite element method 66
3.2* The finite element method in two dimensions 80
3.3 The finite element interpolation and approximation error 93
3.3* The finite element interpolation and approximation error in
two dimensions 130
3.4 The finite element interpolation and approximation: a special case 140
3.4* The interpolation error for the function raip(6) in two dimensions 156
3.5 The description of the mesh and analyses of its optimality 158
3.5* The description of the mesh and analysis of its optimality in
two dimensions 180
3.6 Historical and bibliographical comments 180
4 Local behavior in the finite element method 186
4.0 Introduction 186
4.1 A priori estimates for the nodal errors and the maximum error 189
4.1* A priori estimates for the nodal errors and the maximum error in
two dimensions 200
4.2 A priori estimates for negative norms of the error 201
4.2* A priori estimates for negative norms of the error in two dimensions 223
4.3 Local and pollution error in the finite element solution 227
4.3* The splitting of the error in the two dimensional case 249
4.4 A priori estimates for the pollution error 257
4.4* A priori estimates for the pollution error in two dimensions 279
4.5 Further analysis of the pollution error: Interior estimates 289
x CONTENTS
4.5* The interior estimates in two dimensions 301
4.6 A priori estimates for the local error: superconvergence 302
4.6* Superconvergence in two dimensions 318
4.7 A general approach for the analysis of local behavior of finite
element methods for locally periodic meshes and its applications 320
4.7* A general approach for local asymptotic analysis and analysis of
the superconvergence in two dimensions 338
4.8 Superconvergence via local averaging 381
4.8* Superconvergence based on local recovery: the two dimensional case 398
4.9 Historical and bibliographical comments 411
5 A posteriori estimation of the error 415
5.0 Introduction 415
5.1 The residuum and the construction of lower and upper estimators
for the energy norm of the error 418
5.1* The residuum and the construction of lower and upper estimators
for the energy norm of the error: the two dimensional case 444
5.2 Analysis of the Dirichlet element residual estimator 451
5.2* Analysis of the Dirichlet element residual estimator in two dimensions 475
5.3 Analysis of the Neumann element residual estimator 481
5.3* Analysis of the Neumann element residual estimator in two
dimensions 500
5.4 Subdomain residual estimates 522
5.4* Subdomain residual estimates in two dimensions 535
5.5 Analysis of the explicit element residual estimator 543
5.5* Analysis of the explicit element residual estimator in two dimensions 551
5.6 A posteriori error estimates based on local averaging 563
5.6* A posteriori estimates based on local averaging: the
two dimensional case 568
5.7 The effectivity of the error indicators: the principles for their
comparison and the detailed analysis of their quality 569
5.7* The asymptotic analysis of the effectiveness of the element error
indicators in two dimensions 597
5.8 Historical and bibliographical comments 643
6 Guaranteed a posteriori error estimation and a posteriori
estimation of the pollution error 652
6.0 Introduction 652
6.1 Upper and lower bounds for the energy norm of the error 655
6.1* Upper and lower bounds for the energy norm of the error in
two dimensions 690
6.2 Upper and lower bounds for the error in the output, and
a posteriori estimation of the pollution 717
6.2* Upper and lower bounds for the error in the outputs, and
a posteriori estimation of the pollution error in two dimensions 745
6.3* Historical and bibliographical comments 777
CONTENTS xi
Epilogue 780
Appendix to chapter 2 781
Appendix to chapter 3 787
Glossary of symbols 789
Author Index 792
Subject Index 795
|
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| ctrlnum | (OCoLC)248443473 (DE-599)BVBBV013968362 |
| dewey-full | 620.00151535 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013968362 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:55:19Z |
| institution | BVB |
| isbn | 0198502761 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009561028 |
| oclc_num | 248443473 |
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| owner_facet | DE-703 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-706 DE-11 DE-188 DE-83 DE-20 |
| physical | XI, 802 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Numerical mathematics and scientific computation |
| spelling | Babuška, Ivo 1926-2023 Verfasser (DE-588)104653639 aut The finite element method and its reliability Ivo Babuška and Theofanis Strouboulis 1. publ. Oxford Clarendon Press 2001 XI, 802 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Finite-Elemente-Methode - Zuverlässigkeit Rundungsfehler (DE-588)4465287-2 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Rundungsfehler (DE-588)4465287-2 s DE-604 Strouboulis, Theofanis Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009561028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Babuška, Ivo 1926-2023 Strouboulis, Theofanis The finite element method and its reliability Finite-Elemente-Methode - Zuverlässigkeit Rundungsfehler (DE-588)4465287-2 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4465287-2 (DE-588)4017233-8 |
| title | The finite element method and its reliability |
| title_auth | The finite element method and its reliability |
| title_exact_search | The finite element method and its reliability |
| title_full | The finite element method and its reliability Ivo Babuška and Theofanis Strouboulis |
| title_fullStr | The finite element method and its reliability Ivo Babuška and Theofanis Strouboulis |
| title_full_unstemmed | The finite element method and its reliability Ivo Babuška and Theofanis Strouboulis |
| title_short | The finite element method and its reliability |
| title_sort | the finite element method and its reliability |
| topic | Finite-Elemente-Methode - Zuverlässigkeit Rundungsfehler (DE-588)4465287-2 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite-Elemente-Methode - Zuverlässigkeit Rundungsfehler Finite-Elemente-Methode |
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