Anisotropic finite elements: local estimates and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
Chemnitz
SFB 393
1999
|
| Series: | Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393
[19]99,3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 188 S. graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Apel, Thomas |d 1962- |e Verfasser |0 (DE-588)173318614 |4 aut | |
| 245 | 1 | 0 | |a Anisotropic finite elements |b local estimates and applications |c Thomas Apel. Technische Universität Chemnitz, Sonderforschungsbereich 393, Numerische Simulation auf Massiv Parallelen Rechnern |
| 264 | 1 | |a Chemnitz |b SFB 393 |c 1999 | |
| 300 | |a IV, 188 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393 |v [19]99,3 | |
| 502 | |a Zugl.: Chemnitz, Techn. Univ., Habil.-Schrift, 1999 | ||
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Record in the Search Index
| _version_ | 1807773061704843264 |
|---|---|
| adam_text |
CONTENTS
PREFACE
I
CONTENTS
III
I
PRELIMINARIES
1
1
INTRODUCTION
TO
ANISOTROPIC
FINITE
ELEMENTS
.
1
2
OUTLINE
.
3
3
NOTATION
AND
ANALYTICAL
BACKGROUND
.
9
II
LAGRANGE
INTERPOLATION
ON
ANISOTROPIC
ELEMENTS
15
4
GENERAL
CONSIDERATIONS
.
15
4.1
THE
AIM
OF
THIS
CHAPTER
.
15
4.2
BASIC
TASKS
FOR
PROVING
ANISOTROPIC
INTERPOLATION
ERROR
ESTIMATES
.
17
4.3
BASIC
LEMMATA
.
19
5
TRIANGULAR
ELEMENTS
.
22
6
TETRAHEDRAL
ELEMENTS
.
30
6.1
ERROR
ESTIMATES
IN
CLASSICAL
SOBOLEV
SPACES
.
30
6.2
ERROR
ESTIMATES
IN
WEIGHTED
SOBOLEV
SPACES
.
37
7
QUADRILATERAL
ELEMENTS
.
43
7.1
AFFINE
ELEMENTS
.
43
7.2
RECTANGULAR
ELEMENTS
.
45
7.3
SUBPARAMETRIC
ELEMENTS
.
47
8
HEXAHEDRAL
ELEMENTS
.
51
8.1
AFFINE
ELEMENTS
.
51
8.2
SUBPARAMETRIC
ELEMENTS
.
53
9
PENTAHEDRAL
ELEMENTS
.
54
10
COMMENTS
ON
RELATED
WORK
.
55
III
SCOTT-ZHANG
INTERPOLATION
ON
ANISOTROPIC
ELEMENTS
65
11
GENERAL
CONSIDERATIONS
.
65
11.1
THE
AIM
OF
THIS
CHAPTER
.
65
11.2
DEFINITION
OF
THE
ELEMENT
SIZES
AND
TWO
AUXILIARY
RESULTS
.
66
12
THE
ORIGINAL
SCOTT-ZHANG
OPERATOR
Z
H
.
69
13
THE
OPERATOR
S^
:
CHOOSING
SMALL
SIDES
.
73
13.1
STABILITY
AND
APPROXIMATION
IN
CLASSICAL
SOBOLEV
SPACES
.
73
13.2
STABILITY
IN
WEIGHTED
SOBOLEV
SPACES
.
77
14
THE
OPERATOR
L*:
CHOOSING
LARGE
SIDES
WITH
A
PROJECTION
PROPERTY
.
79
15
THE
OPERATOR
E&:
CHOOSING
LONG
EDGES
IN
THE
THREE-DIMENSIONAL
CASE
.
84
CONTENTS
15.1
STABILITY
AND
APPROXIMATION
IN
CLASSICAL
SOBOLEV
SPACES
.
84
15.2
STABILITY
IN
WEIGHTED
SOBOLEV
SPACES
.
88
16
COMMENTS
ON
RELATED
WORK
.
89
17
COMPARISON
OF
THE
OPERATORS
.
90
IV
ANISOTROPIC
FINITE
ELEMENT
APPROXIMATIONS
NEAR
EDGES
93
18
THE
AIM
OF
THIS
CHAPTER
.
93
19
THE
POISSON
PROBLEM
IN
A
DOMAIN
WITH
AN
EDGE:
AN
INTRODUCTION
.
95
19.1
STATEMENT
OF
THE
PROBLEM
.
95
19.2
LOCAL
MESH
GRADING
IN
TWO
DIMENSIONS
.
98
19.3
ISOTROPIC
AND
ANISOTROPIC
MESH
GRADING
IN
THREE
DIMENSIONS
.
100
20
THE
POISSON
PROBLEM
WITH
EDGE
SINGULARITIES
.
103
20.1
THE
CASE
OF
(MULTI-)LINEAR
TRIAL
FUNCTIONS
.
103
20.2
HIGHER
ORDER
TRIAL
FUNCTIONS
.
107
20.3
CONDITION
NUMBER
OF
THE
STIFFNESS
MATRIX
.
109
21
DIFFUSION
PROBLEMS
IN
DOMAINS
WITH
CORNERS
AND
EDGES
.
ILL
22
THREE
COMMENTS
ON
THE
ANALYTICAL
PROPERTIES
OF
U
.
122
V
ANISOTROPIC
FINITE
ELEMENT
APPROXIMATIONS
IN
BOUNDARY
LAYERS
127
23
THE
AIM
OF
THIS
CHAPTER
.
127
24
DISCRETIZATION
TECHNIQUES
FOR
A
REACTION-DIFFUSION
PROBLEM:
STATE
OF
THE
ART
.
.
129
25
BOUNDARY
LAYERS
AND
CORNER
SINGULARITIES
IN
A
REACTION-DIFFUSION
PROBLEM
.
134
25.1
PROPERTIES
OF
THE
EXACT
SOLUTION
.
134
25.2
INTERPOLATION
ERROR
ESTIMATES
ON
LOCALLY
REFINED
MESHES
.
137
25.3
FINITE
ELEMENT
ERROR
ESTIMATES
.
143
26
A
CONVECTION-DIFFUSION-REACTION
PROBLEM
.
146
26.1
STATEMENT
OF
THE
PROBLEM
.
146
26.2
ERROR
ESTIMATES
FOR
THE
PURE
GALERKIN
METHOD
.
149
26.3
ERROR
ESTIMATES
FOR
A
STABILIZED
GALERKIN
METHOD
.
150
VI
OPEN
PROBLEMS
155
27
A-PRIORI
ERROR
ANALYSIS
AND
FURTHER
APPLICATIONS
.
155
28
A-POSTERIORI
ERROR
ESTIMATES
AND
ADAPTIVE
MESH
REFINEMENT
.
157
29
SOLUTION
OF
THE
ARISING
SYSTEM
OF
LINEAR
EQUATIONS
.
164
30
SHORT
DESCRIPTION
OF
UTILIZED
SOFTWARE
.
171
BIBLIOGRAPHY
175 |
| any_adam_object | 1 |
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| author_GND | (DE-588)173318614 |
| author_facet | Apel, Thomas 1962- |
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| author_sort | Apel, Thomas 1962- |
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| bvnumber | BV012500315 |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)76023414 (DE-599)BVBBV012500315 |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV012500315 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:18:56Z |
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| language | German |
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| physical | IV, 188 S. graph. Darst. |
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| series | Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393 |
| series2 | Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393 |
| spelling | Apel, Thomas 1962- Verfasser (DE-588)173318614 aut Anisotropic finite elements local estimates and applications Thomas Apel. Technische Universität Chemnitz, Sonderforschungsbereich 393, Numerische Simulation auf Massiv Parallelen Rechnern Chemnitz SFB 393 1999 IV, 188 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393 [19]99,3 Zugl.: Chemnitz, Techn. Univ., Habil.-Schrift, 1999 Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Anisotropie (DE-588)4002073-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Elliptisches Randwertproblem (DE-588)4193399-0 s Anisotropie (DE-588)4002073-3 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393 [19]99,3 (DE-604)BV011242617 1999,3 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008486342&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Apel, Thomas 1962- Anisotropic finite elements local estimates and applications Sonderforschungsbereich Numerische Simulation auf Massiv Parallelen Rechnern <Chemnitz>: Preprint-Reihe des Chemnitzer SFB 393 Elliptisches Randwertproblem (DE-588)4193399-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Anisotropie (DE-588)4002073-3 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4017233-8 (DE-588)4002073-3 (DE-588)4113937-9 |
| title | Anisotropic finite elements local estimates and applications |
| title_auth | Anisotropic finite elements local estimates and applications |
| title_exact_search | Anisotropic finite elements local estimates and applications |
| title_full | Anisotropic finite elements local estimates and applications Thomas Apel. Technische Universität Chemnitz, Sonderforschungsbereich 393, Numerische Simulation auf Massiv Parallelen Rechnern |
| title_fullStr | Anisotropic finite elements local estimates and applications Thomas Apel. Technische Universität Chemnitz, Sonderforschungsbereich 393, Numerische Simulation auf Massiv Parallelen Rechnern |
| title_full_unstemmed | Anisotropic finite elements local estimates and applications Thomas Apel. Technische Universität Chemnitz, Sonderforschungsbereich 393, Numerische Simulation auf Massiv Parallelen Rechnern |
| title_short | Anisotropic finite elements |
| title_sort | anisotropic finite elements local estimates and applications |
| title_sub | local estimates and applications |
| topic | Elliptisches Randwertproblem (DE-588)4193399-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Anisotropie (DE-588)4002073-3 gnd |
| topic_facet | Elliptisches Randwertproblem Finite-Elemente-Methode Anisotropie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008486342&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011242617 |
| work_keys_str_mv | AT apelthomas anisotropicfiniteelementslocalestimatesandapplications |