A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin
Logos-Verl.
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Chemnitz, Techn. Univ., Diss., 1999 |
| Physical Description: | 127 S. graph. Darst. |
| ISBN: | 3897221802 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012430167 | ||
| 003 | DE-604 | ||
| 005 | 19990907 | ||
| 007 | t | ||
| 008 | 990223s1999 gw d||| m||| 00||| ger d | ||
| 016 | 7 | |a 955820588 |2 DE-101 | |
| 020 | |a 3897221802 |c kart. : DM 79.00, sfr 71.90, S 576.70 |9 3-89722-180-2 | ||
| 035 | |a (OCoLC)231788155 | ||
| 035 | |a (DE-599)BVBBV012430167 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-12 | ||
| 100 | 1 | |a Kunert, Gerd |d 1970- |e Verfasser |0 (DE-588)120839113 |4 aut | |
| 245 | 1 | 0 | |a A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes |c von Gerd Kunert |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 1999 | |
| 300 | |a 127 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Zugl.: Chemnitz, Techn. Univ., Diss., 1999 | ||
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Poisson-Gleichung |0 (DE-588)4174972-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Singuläre Störung |0 (DE-588)4055100-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a A-posteriori-Abschätzung |0 (DE-588)4346907-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fehlerabschätzung |0 (DE-588)4228085-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Anisotropie |0 (DE-588)4002073-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Reaktions-Diffusionsgleichung |0 (DE-588)4323967-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Poisson-Gleichung |0 (DE-588)4174972-8 |D s |
| 689 | 0 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | 2 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | 3 | |a Anisotropie |0 (DE-588)4002073-3 |D s |
| 689 | 0 | 4 | |a Fehlerabschätzung |0 (DE-588)4228085-0 |D s |
| 689 | 0 | 5 | |a A-posteriori-Abschätzung |0 (DE-588)4346907-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Reaktions-Diffusionsgleichung |0 (DE-588)4323967-5 |D s |
| 689 | 1 | 1 | |a Singuläre Störung |0 (DE-588)4055100-3 |D s |
| 689 | 1 | 2 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 1 | 3 | |a Anisotropie |0 (DE-588)4002073-3 |D s |
| 689 | 1 | 4 | |a Fehlerabschätzung |0 (DE-588)4228085-0 |D s |
| 689 | 1 | 5 | |a A-posteriori-Abschätzung |0 (DE-588)4346907-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008435308 | |
Record in the Search Index
| _version_ | 1807773059045654528 |
|---|---|
| adam_text |
CONTENTS
LIST
OF
SYMBOLS
.
7
1
INTRODUCTION
9
1.1
INTRODUCTION
TO
ANISOTROPIC
FINITE
ELEMENTS
.
9
1.2
AIM
OF
THIS
WORK
AND
OUTLINE
.
13
2
PRELIMINARIES
17
2.1
NOTATION
AND
BASIC
PROPERTIES
.
17
2.1.1
NOTATION
OF
THE
TETRAHEDRON
.
17
2.1.2
TRANSFORMATIONE
.
19
2.1.3
THE
DIRECTIONAL
DERIVATIVE
D
T
.
21
2.1.4
NOTATION
OF
THE
SUMMATION
.
22
2.1.5
AUXILIARY
SUBDOMAINS
.
23
2.2
REQUIREMENTS
ON
THE
MESH
.
23
2.3
BASIC
TOOLS
.
24
2.3.1
ANISOTROPIC
TRACE
INEQUALITIES
.
24
2.3.2
INVERSE
INEQUALITIES
FOR
FINITE
ELEMENT
FUNCTIONS
.
26
2.3.3
BUBBLE
FUNCTIONS
.
27
3
THE
POISSON
EQUATION
31
3.1
ANALYTICAL
BACKGROUND
.
31
3.2
RESIDUAL
ERROR
ESTIMATOR
.
34
3.2.1
RELATION
BETWEEN
ANISOTROPIC
MESH
AND
ANISOTROPIC
FUNCTION
.
34
3.2.2
ANISOTROPIC
INTERPOLATION
ESTIMATES
.
37
3.2.3
ANISOTROPIC
RESIDUAL
ERROR
ESTIMATOR
.
47
3.2.4
DISCUSSION
OF
THE
MATCHING
FUNCTION
.
53
3.3
A
LOCAL
DIRICHLET
PROBLEM
ERROR
ESTIMATOR
.
55
3.3.1
INTRODUCTION
AND
DEFINITION
.
55
3.3.2
PRELIMINARY
RESULT
.
58
3.3.3
EQUIVALENCE
AND
BOUNDS
OF
THE
ESTIMATOR
.
63
3.3.4
CONDITION
NUMBER
OF
THE
FINITE
ELEMENT
MATRIX
.
67
3.3.5
COMMENTS
AND
REMARKS
.
69
3.4
ZIENKIEWICZ-ZHU
LIKE
ERROR
ESTIMATORS
.
71
3.4.1
INTRODUCTION
.
71
3.4.2
CUBOIDAL
OR
RECTANGULAR
MESH
.
71
3.4.3
TETRAHEDRAL
OR
TRIANGULAR
MESHES
.
72
3.4.4
CONCLUSIONS
.
74
3.5
L
2
ERROR
ESTIMATOR
.
75
3.5.1
SPECIAL
L
2
BUBBLE
FUNCTIONS
AND
THEIR
INVERSE
INEQUALITIES
.
75
3.5.2
THE
MATCHING
FUNCTION
FOR
2
ERROR
ESTIMATION
.
79
6
CONTENTS
3.5.3
ANISOTROPIE
INTERPOLATION
ESTIMATES
.
80
3.5.4
ANISOTROPIE
I
2
ERROR
ESTIMATOR
.
82
4
A
REACTION-DIFFUSION
EQUATION
85
4.1
ANALYTICAL
BACKGROUND
.
85
4.2
RESIDUAL
ERROR
ESTIMATOR
.
87
4.2.1
SPECIAL
FACE
BUBBLE
FUNCTIONS
.
87
4.2.2
ANISOTROPIE
INTERPOLATION
ESTIMATES
.
88
4.2.3
ANISOTROPIE
RESIDUAL
ERROR
ESTIMATOR
.
89
5
NUMERICAL
EXAMPLES
93
5.1
SCOPE
OF
AND
INTRODUCTION
TO
THE
NUMERICAL
EXPERIMENTS
.
93
5.1.1
GENERAL
REMARKS
.
93
5.1.2
THE
MATCHING
FUNCTIONS
MI
AND
M
2
.
94
5.1.3
INTERPOLATION
ERROR
ESTIMATES
.
95
5.1.4
FINITE
ELEMENT
ERROR
ESTIMATES
.
95
5.1.5
COMPUTATIONAL
EFFORT
.
97
5.1.6
AIM
OF
THE
EXPERIMENTS
.
97
5.2
NUMERICAL
EXAMPLES
.
99
5.2.1
EXAMPLE
1
(2D;
ANISOTROPIC
SOLUTION
AND
ADAPTED
MESH)
.
99
5.2.2
EXAMPLE
2
(2D;
ANISOTROPIC
SOLUTION
AND
MISADAPTED
MESH)
.
107
5.2.3
EXAMPLE
3
(2D;
ISOTROPIC
SOLUTION
AND
ANISOTROPIC
MESH)
.
111
5.2.4
EXAMPLE
4
(3D;
ANISOTROPIC
SOLUTION
AND
ADAPTED
MESH)
.
113
5.3
CONCLUSIONS
.
119
SUMMARY
121
BIBLIOGRAPHY
123 |
| any_adam_object | 1 |
| author | Kunert, Gerd 1970- |
| author_GND | (DE-588)120839113 |
| author_facet | Kunert, Gerd 1970- |
| author_role | aut |
| author_sort | Kunert, Gerd 1970- |
| author_variant | g k gk |
| building | Verbundindex |
| bvnumber | BV012430167 |
| ctrlnum | (OCoLC)231788155 (DE-599)BVBBV012430167 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV012430167</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19990907</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990223s1999 gw d||| m||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">955820588</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3897221802</subfield><subfield code="c">kart. : DM 79.00, sfr 71.90, S 576.70</subfield><subfield code="9">3-89722-180-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)231788155</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012430167</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kunert, Gerd</subfield><subfield code="d">1970-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)120839113</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes</subfield><subfield code="c">von Gerd Kunert</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">Logos-Verl.</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">127 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Zugl.: Chemnitz, Techn. Univ., Diss., 1999</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Poisson-Gleichung</subfield><subfield code="0">(DE-588)4174972-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Singuläre Störung</subfield><subfield code="0">(DE-588)4055100-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">A-posteriori-Abschätzung</subfield><subfield code="0">(DE-588)4346907-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fehlerabschätzung</subfield><subfield code="0">(DE-588)4228085-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Anisotropie</subfield><subfield code="0">(DE-588)4002073-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reaktions-Diffusionsgleichung</subfield><subfield code="0">(DE-588)4323967-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Poisson-Gleichung</subfield><subfield code="0">(DE-588)4174972-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Anisotropie</subfield><subfield code="0">(DE-588)4002073-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="4"><subfield code="a">Fehlerabschätzung</subfield><subfield code="0">(DE-588)4228085-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="5"><subfield code="a">A-posteriori-Abschätzung</subfield><subfield code="0">(DE-588)4346907-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Reaktions-Diffusionsgleichung</subfield><subfield code="0">(DE-588)4323967-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Singuläre Störung</subfield><subfield code="0">(DE-588)4055100-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="3"><subfield code="a">Anisotropie</subfield><subfield code="0">(DE-588)4002073-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="4"><subfield code="a">Fehlerabschätzung</subfield><subfield code="0">(DE-588)4228085-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="5"><subfield code="a">A-posteriori-Abschätzung</subfield><subfield code="0">(DE-588)4346907-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008435308</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV012430167 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:18:53Z |
| institution | BVB |
| isbn | 3897221802 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008435308 |
| oclc_num | 231788155 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 127 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Logos-Verl. |
| record_format | marc |
| spelling | Kunert, Gerd 1970- Verfasser (DE-588)120839113 aut A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes von Gerd Kunert Berlin Logos-Verl. 1999 127 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zugl.: Chemnitz, Techn. Univ., Diss., 1999 Randwertproblem (DE-588)4048395-2 gnd rswk-swf Poisson-Gleichung (DE-588)4174972-8 gnd rswk-swf Singuläre Störung (DE-588)4055100-3 gnd rswk-swf A-posteriori-Abschätzung (DE-588)4346907-3 gnd rswk-swf Fehlerabschätzung (DE-588)4228085-0 gnd rswk-swf Anisotropie (DE-588)4002073-3 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Poisson-Gleichung (DE-588)4174972-8 s Randwertproblem (DE-588)4048395-2 s Finite-Elemente-Methode (DE-588)4017233-8 s Anisotropie (DE-588)4002073-3 s Fehlerabschätzung (DE-588)4228085-0 s A-posteriori-Abschätzung (DE-588)4346907-3 s DE-604 Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Singuläre Störung (DE-588)4055100-3 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kunert, Gerd 1970- A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes Randwertproblem (DE-588)4048395-2 gnd Poisson-Gleichung (DE-588)4174972-8 gnd Singuläre Störung (DE-588)4055100-3 gnd A-posteriori-Abschätzung (DE-588)4346907-3 gnd Fehlerabschätzung (DE-588)4228085-0 gnd Anisotropie (DE-588)4002073-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4174972-8 (DE-588)4055100-3 (DE-588)4346907-3 (DE-588)4228085-0 (DE-588)4002073-3 (DE-588)4017233-8 (DE-588)4323967-5 (DE-588)4113937-9 |
| title | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes |
| title_auth | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes |
| title_exact_search | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes |
| title_full | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes von Gerd Kunert |
| title_fullStr | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes von Gerd Kunert |
| title_full_unstemmed | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes von Gerd Kunert |
| title_short | A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes |
| title_sort | a posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes |
| topic | Randwertproblem (DE-588)4048395-2 gnd Poisson-Gleichung (DE-588)4174972-8 gnd Singuläre Störung (DE-588)4055100-3 gnd A-posteriori-Abschätzung (DE-588)4346907-3 gnd Fehlerabschätzung (DE-588)4228085-0 gnd Anisotropie (DE-588)4002073-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd |
| topic_facet | Randwertproblem Poisson-Gleichung Singuläre Störung A-posteriori-Abschätzung Fehlerabschätzung Anisotropie Finite-Elemente-Methode Reaktions-Diffusionsgleichung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kunertgerd aposteriorierrorestimationforanisotropictetrahedralandtriangularfiniteelementmeshes |