A posteriori error estimation techniques for finite element methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2013
|
| Edition: | 1. publ. |
| Series: | Numerical mathematics and scientific computation
Oxford science publications |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 373 - 386 |
| Physical Description: | XX, 393 S. graph. Darst. |
| ISBN: | 9780199679423 |
Staff View
MARC
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| 490 | 0 | |a Numerical mathematics and scientific computation | |
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| 653 | |a Error analysis (Mathematics) | ||
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Record in the Search Index
| _version_ | 1804150485991555072 |
|---|---|
| adam_text | CONTENTS
1
A Simple
Model Problem
..................................1
1.1
Motivation
and Overview
1
1.2
The Model Problem and its Discretisation
4
1.3
Notations and Auxiliary Results
5
1.4
Residual Estimates
10
1.5
A Vertex-Oriented Residual Error Indicator
17
1.6
Edge Residuals
20
1.7
Auxiliary Local Problems
25
1.8
A Hierarchical Approach
31
1.9
Gradient Recovery
36
1.10
Equilibrated
Resi
duals
41
1.11
Dual Weighted Residuals
45
1.12
The Hyper-Circle Method
48
1.13
Efficiency and Asymptotic Exactness
53
1.14
Convergence of the Adaptive Process I
58
1.15
Summary and Outlook
62
2
Implementation
.......................................64
2.1
Mesh-Refinement
64
2.2
Mesh-Coarsening
69
2.3
Mesh-Smoothing
70
2.4
Data Structures
74
2.5
Numerical Examples
76
3
Auxiliary Results
......................................79
3.1
Function Spaces
79
3.2
Finite Element Meshes and Spaces
31
3.3
Trace Inequalities
87
3.4
Poincaré
andFriedrichs Inequalities
91
3.5
Interpolation Error Estimates
108
3.6
Inverse Estimates
H
2
3.7
Decomposition of
Affine
Functions in V(0, l;Y*)
130
3.8
Estimation of Residuals
132
4
Linear Elliptic Equations
................................151
4.1
Abstract Linear Problems
151
4.2
The Model Problem Revisited
157
43
Reaction-Difiusion Equations
159
4.4
Convection-Diffusion Equations
163
4.5 Anisotropie
Meshes
177
4.6
Non-Smooth Coefficients
191
4.7
Eigenvalue Problems
205
XX I CONTENTS
4.8
Mixed Formulation of the
Poisson
Equation
208
4.9
The Equations of Linear Elasticity
223
4Л0
The Stokes Equations
237
4.11
The Bi-harmonic Equation
248
4.12
Non-Conforming Discretisations
261
4.13
Convergence of the Adaptive Process II
264
5
Nonlinear Elliptic Equations
..............................281
5.1 Abstract Nonlinear Problems
281
5.2 Quasilinear
Equations of Second Order
290
5.3
Eigenvalue Problems Revisited
299
5.4
The Stationary Navier-Stokes Equations
301
6
Parabolic Equations
...................................309
6.1
The Heat Equation
309
6.2
Time-Dependent Convection-Diffusion Equations
317
6.3
Linear Parabolic Equations of Second Order
326
6.4
The Method of Characteristics
329
6.5
The Time-Dependent Stokes Equations
335
6.6
Nonlinear Parabolic Equations of Second Order
347
6.7
Finite Volume Methods
360
6.8
Convergence of the Adaptive Process III
362
References
373
List of Symbols
387
Index
390
NUMERICAL MATHEMATICS AND SCIENTIFIC COMPUTATION is
a series designed
lo
provide texts and monographs for graduate students
and researchers on a wide range of mathematical topic sat the interface
of computational science and numerical analysis.
Λ
Posteriori Error Estimation Techniques for Finite Element Methods
Rüdiger
Verfurtn
Self-Adaptive discretization methods are now an indispensable tool tor the
numerical solution of partial differential equations thai
arisi1 troni
physical and
technical applications. The aim is to obtain a numerical solution within a prescribed
tolerance
usi
ιιμ <ι
minimal amount of work. The main tools in achieving this goal are
a posteriori error estimates v» hich give global and local information on the error of
the numerical solution and which can easily be computed from the given numerical
solution and the data of the differential equation.
This hook reviews the most frequently used a posteriori error estimation
techniques and applies them to a broad class of linear and nonlinear elliptic and
parabolic equations. Although there are
¿irions
approaches to adapth itv and a
posteriori error estimation, they arc all based on a Few common principles. The main
aim of the hook is to elaborate these basic principles ;u ( to give guidelines for
developing adaptive schemes for new problems.
Chapters I and
2
are quite
elementarv
and present various error indicators and
their use for mesh adaptation in tin1 framework of a simple model problem. The
basic principles are introduced using a minimal amount of notations and techniques
providing a complete overv iew for the non-specialist Chapters
4-6
on the other hand
are more
adi
anced and present a posteriori error estimates within a genera]
framework using the technical tools collected in Chapters. Most sections (lose
with a bibliographical remark which indicates the historical development
and hints at further results.
Rüdiger
Verfurth is Full
Professorin
the Pacult) of Mathematics,
Ruhr-1
sitiit Bochum,
Germany.
Elrror control and adaptive solution algorithms for
ß
η
ite
element
approximation are
¿ι
hey concern of every practitioner, the present text,
written by a leading authority in
t
/ie
tittle! who has made many important
contributions, will be valuable tor theoreticians and practitioners alike.
Mark Ainswnrth. Professor ol Applied Mathematics, Brown University
|
| any_adam_object | 1 |
| author | Verfürth, Rüdiger 1955- |
| author_GND | (DE-588)141710780 |
| author_facet | Verfürth, Rüdiger 1955- |
| author_role | aut |
| author_sort | Verfürth, Rüdiger 1955- |
| author_variant | r v rv |
| building | Verbundindex |
| bvnumber | BV041103170 |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)855552009 (DE-599)HBZHT017631348 |
| 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 | 3518.25 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV041103170 |
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| indexdate | 2024-07-10T00:39:41Z |
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| isbn | 9780199679423 |
| language | English |
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| spelling | Verfürth, Rüdiger 1955- Verfasser (DE-588)141710780 aut A posteriori error estimation techniques for finite element methods Rüdiger Verfürth 1. publ. Oxford Oxford Univ. Press 2013 XX, 393 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Oxford science publications Literaturverz. S. 373 - 386 Fehlerabschätzung (DE-588)4228085-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite element method. Error analysis (Mathematics) Finite-Elemente-Methode (DE-588)4017233-8 s Fehlerabschätzung (DE-588)4228085-0 s DE-604 DE-601 pdf/application http://zbmath.org/?q=an:1279.65127 Zentralblatt MATH Inhaltstext 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=026079521&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=026079521&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Verfürth, Rüdiger 1955- A posteriori error estimation techniques for finite element methods Fehlerabschätzung (DE-588)4228085-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4228085-0 (DE-588)4017233-8 |
| title | A posteriori error estimation techniques for finite element methods |
| title_auth | A posteriori error estimation techniques for finite element methods |
| title_exact_search | A posteriori error estimation techniques for finite element methods |
| title_full | A posteriori error estimation techniques for finite element methods Rüdiger Verfürth |
| title_fullStr | A posteriori error estimation techniques for finite element methods Rüdiger Verfürth |
| title_full_unstemmed | A posteriori error estimation techniques for finite element methods Rüdiger Verfürth |
| title_short | A posteriori error estimation techniques for finite element methods |
| title_sort | a posteriori error estimation techniques for finite element methods |
| topic | Fehlerabschätzung (DE-588)4228085-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Fehlerabschätzung Finite-Elemente-Methode |
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