Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2000
|
| Series: | Berichte aus der Informatik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | II, 131 S. graph. Darst. : 21 cm |
| ISBN: | 382657513X |
Staff View
MARC
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| 100 | 1 | |a Schneider, Stefan-Alexander |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements |c Stefan-Alexander Schneider |
| 264 | 1 | |a Aachen |b Shaker |c 2000 | |
| 300 | |a II, 131 S. |b graph. Darst. : 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Informatik | |
| 502 | |a Zugl.: München, Techn. Univ., Diss., 2000 | ||
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Record in the Search Index
| _version_ | 1807772779373658112 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
2
HIERARCHICAL
FINITE
ELEMENTS
9
2.1
THE
MULTIDIMENSIONAL
HIERARCHICAL
BASIS
.
9
2.1.1
THE
ONE-DIMENSIONAL,
PIECEWISE
LINEAR
HIERARCHICAL
BASIS
.
9
2.1.2
THE
MULTIDIMENSIONAL,
PIECEWISE
MULTILINEAR
HIERARCHICAL
BASIS
.
.
11
2.1.3
SOME
REMARKS
ON
HIERARCHICAL
POLYNOMIAL
BASES
.
12
2.2
THE
MODEL
PROBLEM
.
15
2.3
A
REDUCTION
FORMULA
FOR
THE
MULTIDIMENSIONAL
INTEGRATION
.
16
3
ADAPTATION
19
3.1
THE
DISCRETIZATION
ERROR
.
21
3.2
THE
ERROR
DECOMPOSITION
.
23
3.3
THE
ERROR
ESTIMATION
.
27
3.4
THE
GRID
REFINEMENT
.
31
3.4.1
THE
REFINEMENT
OF
AN
ELEMENT
.
31
3.4.2
THE
INDICATION
OF
AN
ELEMENT
.
33
3.5
THE
SELF-ADAPTIVE
ALGORITHM
.
34
3.6
SOME
REMARKS
ON
REGULAR
SPARSE
GRIDS
.
38
3.6.1
A
DEFINITION
OF
REGULAR
SPARSE
GRIDS
.
39
3.6.2
A
FORMULA
FOR
THE
NUMBER
OF
DEGREES
OF
FREEDOM
A'F
REE
.
39
4
MULTIGRID
SOLVER
43
4.1
THE
ERROR
SMOOTHING
.
44
4.2
THE
RESTRICTION
AND
PROLONGATION
.
44
4.3
THE
CONVERGENCE
RATE
P
.
45
5
ALGORITHMIC
ASPECTS
47
5.1
THE
ONE-DIMENSIONAL
DATA
STRUCTURE
.
48
5.2
THE
ONE-DIMENSIONAL
TRAVERSAL
.
49
5.2.1
OPERATIONS
ON
LINES
.
51
5.2.2
OPERATIONS
ON
NODES
.
54
5.2.3
SUMMARY
.
55
5.3
THE
MATRIX-VECTOR
PRODUCT
.
55
5.3.1
THE
TOP-DOWN
PARSING
.
58
5.3.2
THE
BOTTOM-UP
PARSING
.
60
5.3.3
AN
EXAMPLE:
MULTIGRID
SOLVER
FOR
LINEAR
FINITE
ELEMENTS
.
65
5.3.4
SUMMARY
.
68
5.4
THE
MULTIDIMENSIONAL
DATA
STRUCTURE
.
69
5.5
THE
MULTIDIMENSIONAL
TRAVERSAL
.
72
5.6
UNIDIRECTIONAL
ALGORITHMS
.
73
II
CONTENTS
5.7
THE
MULTIDIMENSIONAL
REFINEMENT
.
76
5.7.1
THE
ONE-DIMENSIONAL
CASE
.
76
5.7.2
THE
MULTIDIMENSIONAL
CASE
.
76
5.8
SUMMARY
.
77
6
NUMERICAL
EXAMPLES
79
6.1
A
SMOOTH
TWO-DIMENSIONAL
LAPLACE
PROBLEM
.
80
6.1.1
THE
FULL
GRID
APPROXIMATION
.
80
6.1.2
THE
ADAPTIVE
POINT-VALUE
APPROXIMATION
.
81
6.1.3
THE
REGULAR
SPARSE
GRID
APPROXIMATION
.
83
6.1.4
THE
ADAPTIVE
^-APPROXIMATION
.
87
6.1.5
SUMMARY
.
89
6.2
A
SMOOTH
TWO-DIMENSIONAL
POISSON
PROBLEM
.
92
6.2.1
THE
FULL
GRID
APPROXIMATION
.
92
6.2.2
THE
ADAPTIVE
POINT-VALUE
APPROXIMATION
.
93
6.3
THE
ADAPTIVE
POINT-VALUE
APPROXIMATION
FOR
A
ROOT
SINGULARITY
.
95
6.4
THE
ADAPTIVE
^-APPROXIMATION
FOR
A
SINGULARITY
.
98
6.5
A
VARIABLE
DIFFUSION
COEFFICIENT
PROBLEM
.
99
6.6
A
P-ASYMPTOTIC
APPROXIMATION
.
101
6.7
THE
THREE-DIMENSIONAL
LAPLACE
PROBLEM
.
103
6.7.1
THE
REGULAR
SPARSE
GRID
APPROXIMATION
.
103
6.7.2
THE
ADAPTIVE
ENERGY-APPROXIMATION
.
103
7
APPLICATIONS
TO
FLUID
DYNAMICS
105
7.1
THE
STOKES
EQUATIONS
.
106
7.2
THE
DISCRETIZATION
.
107
7.3
THE
ADAPTATION
.
108
7.4
NUMERICAL
EXAMPLES
.
109
7.4.1
THE
TWO-DIMENSIONAL
COUETTE
FLOW
.
110
7.4.2
THE
TWO-DIMENSIONAL
LID-DRIVEN
CAVITY
.
ILL
7.4.3
THE
THREE-DIMENSIONAL
LID-DRIVEN
CAVITY
.
114
7.5
SUMMARY
.
119
8
CONCLUDING
REMARKS
125
BIBLIOGRAPHY
127 |
| any_adam_object | 1 |
| author | Schneider, Stefan-Alexander |
| author_facet | Schneider, Stefan-Alexander |
| author_role | aut |
| author_sort | Schneider, Stefan-Alexander |
| author_variant | s a s sas |
| building | Verbundindex |
| bvnumber | BV013218884 |
| classification_tum | MAT 354d |
| ctrlnum | (OCoLC)48478633 (DE-599)BVBBV013218884 |
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| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV013218884 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:14:28Z |
| institution | BVB |
| isbn | 382657513X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009007442 |
| oclc_num | 48478633 |
| open_access_boolean | |
| owner | DE-703 DE-12 DE-91 DE-BY-TUM DE-706 DE-634 |
| owner_facet | DE-703 DE-12 DE-91 DE-BY-TUM DE-706 DE-634 |
| physical | II, 131 S. graph. Darst. : 21 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Shaker |
| record_format | marc |
| series2 | Berichte aus der Informatik |
| spelling | Schneider, Stefan-Alexander Verfasser aut Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements Stefan-Alexander Schneider Aachen Shaker 2000 II, 131 S. graph. Darst. : 21 cm txt rdacontent n rdamedia nc rdacarrier Berichte aus der Informatik Zugl.: München, Techn. Univ., Diss., 2000 Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Adaptives Gitter (DE-588)4333769-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Elliptische Differentialgleichung (DE-588)4014485-9 s Finite-Elemente-Methode (DE-588)4017233-8 s Adaptives Gitter (DE-588)4333769-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schneider, Stefan-Alexander Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements Finite-Elemente-Methode (DE-588)4017233-8 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Adaptives Gitter (DE-588)4333769-7 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4014485-9 (DE-588)4333769-7 (DE-588)4113937-9 |
| title | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements |
| title_auth | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements |
| title_exact_search | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements |
| title_full | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements Stefan-Alexander Schneider |
| title_fullStr | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements Stefan-Alexander Schneider |
| title_full_unstemmed | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements Stefan-Alexander Schneider |
| title_short | Adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements |
| title_sort | adaptive solution of elliptic partial differential equations by hierarchical tensor product finite elements |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Adaptives Gitter (DE-588)4333769-7 gnd |
| topic_facet | Finite-Elemente-Methode Elliptische Differentialgleichung Adaptives Gitter Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schneiderstefanalexander adaptivesolutionofellipticpartialdifferentialequationsbyhierarchicaltensorproductfiniteelements |