The mathematical theory of finite element methods:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg
Springer
1996
|
| Ausgabe: | Corr. 2. print. |
| Schriftenreihe: | Texts in applied mathematics
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 287 - 291 |
| Beschreibung: | XII, 297 S. graph. Darst. |
| ISBN: | 3540941932 0387941932 |
Internformat
MARC
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| 084 | |a MAT 674f |2 stub | ||
| 100 | 1 | |a Brenner, Susanne C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The mathematical theory of finite element methods |c Susanne C. Brenner ; L. Ridgway Scott |
| 250 | |a Corr. 2. print. | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg |b Springer |c 1996 | |
| 300 | |a XII, 297 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts in applied mathematics |v 15 | |
| 500 | |a Literaturverz. S. 287 - 291 | ||
| 650 | 7 | |a Analise numerica |2 larpcal | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Finite element method |x Mathematics | |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Scott, L. Ridgway |e Verfasser |0 (DE-588)124153356 |4 aut | |
| 830 | 0 | |a Texts in applied mathematics |v 15 |w (DE-604)BV002476038 |9 15 | |
| 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=007683459&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805067849485516800 |
|---|---|
| adam_text |
CONTENTS
PREFACE
.
VII
0
BASIC
CONCEPTS
.
1
0.1
WEAK
FORMULATION
OF
BOUNDARY
VALUE
PROBLEMS
.
1
0.2
RITZ-GALERKIN
APPROXIMATION
.
3
0.3
ERROR
ESTIMATES
.
4
0.4
PIECEWISE
POLYNOMIAL
SPACES
-
THE
FINITE
ELEMENT
METHOD
.
7
0.5
RELATIONSHIP
TO
DIFFERENCE
METHODS
.
9
0.6
COMPUTER
IMPLEMENTATION
OF
FINITE
ELEMENT
METHODS
.
10
0.7
LOCAL
ESTIMATES
.
12
0.8
WEIGHTED
NORM
ESTIMATES
.
13
0.X
EXERCISES
.
18
1
SOBOLEV
SPACES
.
21
1.1
REVIEW
OF
LEBESGUE
INTEGRATION
THEORY
.
21
1.2
GENERALIZED
(WEAK)
DERIVATIVES
.
24
1.3
SOBOLEV
NORMS
AND
ASSOCIATED
SPACES
.
27
1.4
INCLUSION
RELATIONS
AND
SOBOLEV
'
S
INEQUALITY
.
30
1.5
REVIEW
OF
CHAPTER
0
.
33
1.6
TRACE
THEOREMS
.
34
1.7
NEGATIVE
NORMS
AND
DUALITY
.
38
1.X
EXERCISES
.
40
2
VARIATIONAL
FORMULATION
OF
ELLIPTIC
BOUNDARY
VALUE
PROBLEMS
.
47
2.1
INNER-PRODUCT
SPACES
.
47
2.2
HILBERT
SPACES
.
49
2.3
PROJECTIONS
ONTO
SUBSPACES
.
50
X
CONTENTS
2.4
RIESZ
REPRESENTATION
THEOREM
.
53
2.5
FORMULATION
OF
SYMMETRIC
VARIATIONAL
PROBLEMS
.
54
2.6
FORMULATION
OF
NONSYMMETRIC
VARIATIONAL
PROBLEMS
.
57
2.7
THE
LAX-MILGRAM
THEOREM
.
58
2.8
ESTIMATES
FOR
GENERAL
FINITE
ELEMENT
APPROXIMATION
.
62
2.9
HIGHER-DIMENSIONAL
EXAMPLES
.
63
2.X
EXERCISES
.
65
3
THE
CONSTRUCTION
OF
A
FINITE
ELEMENT
SPACE
.
67
3.1
THE
FINITE
ELEMENT
.
67
3.2
TRIANGULAR
FINITE
ELEMENTS
.
69
THE
LAGRANGE
ELEMENT
.
70
THE
HERMITE
ELEMENT
.
73
THE
ARGYRIS
ELEMENT
.
74
3.3
THE
INTERPOLANT
.
75
3.4
EQUIVALENCE
OF
ELEMENTS
.
79
3.5
RECTANGULAR
ELEMENTS
.
82
TENSOR
PRODUCT
ELEMENTS
.
83
THE
SERENDIPITY
ELEMENT
.
84
3.6
HIGHER-DIMENSIONAL
ELEMENTS
.
85
3.7
EXOTIC
ELEMENTS
.
87
3.X
EXERCISES
.
87
4
POLYNOMIAL
APPROXIMATION
THEORY
IN
SOBOLEV
SPACES
.
91
4.1
AVERAGED
TAYLOR
POLYNOMIALS
.
91
4.2
ERROR
REPRESENTATION
.
94
4.3
BOUNDS
FOR
RIESZ
POTENTIALS
.
98
4.4
BOUNDS
FOR
THE
INTERPOLATION
ERROR
.
103
4.5
INVERSE
ESTIMATES
.
109
4.6
TENSOR-PRODUCT
POLYNOMIAL
APPROXIMATION
.
112
4.7
ISOPARAMETRIC
POLYNOMIAL
APPROXIMATION
.
117
4.8
INTERPOLATION
OF
NON-SMOOTH
FUNCTIONS
.
118
4.X
EXERCISES
.
120
5
N-DIMENSIONAL
VARIATIONAL
PROBLEMS
.
123
5.1
VARIATIONAL
FORMULATION
OF POISSON
'
S
EQUATION
.
123
5.2
VARIATIONAL
FORMULATION
OF
THE
PURE
NEUMANN
PROBLEM
.
126
5.3
COERCIVITY
OF
THE
VARIATIONAL
PROBLEM
.
128
CONTENTS
XI
5.4
VARIATIONAL
APPROXIMATION
OF
POISSON
'
S
EQUATION
.
130
5.5
ELLIPTIC
REGULARITY
ESTIMATES
.
133
5.6
GENERAL
SECOND-ORDER
ELLIPTIC
OPERATORS
.
135
5.7
VARIATIONAL
APPROXIMATION
OF
GENERAL
ELLIPTIC
PROBLEMS
.
138
5.8
NEGATIVE-NORM
ESTIMATES
.
140
5.9
THE
PLATE-BENDING
BIHARMONIC
PROBLEM
.
142
5.X
EXERCISES
.
146
6
FINITE
ELEMENT
MULTIGRID
METHODS
.
149
6.1
A
MODEL
PROBLEM
.
149
6.2
MESH-DEPENDENT
NORMS
.
150
6.3
THE
MULTIGRID
ALGORITHM
.
152
6.4
APPROXIMATION
PROPERTY
.
155
6.5
W-CYCLE
CONVERGENCE
FOR
THE
FC
TH
LEVEL
ITERATION
.
156
6.6
V-CYCLE
CONVERGENCE
FOR
THE
A:
TH
LEVEL
ITERATION
.
159
6.7
FULL
MULTIGRID
CONVERGENCE
ANALYSIS
AND
WORK
ESTIMATES
.
164
6.X
EXERCISES
.
166
7
MAX-NORM
ESTIMATES
.
169
7.1
MAIN
THEOREM
.
169
7.2
REDUCTION
TO
WEIGHTED
ESTIMATES
.
172
7.3
PROOF
OF
LEMMA
7.2.6
.
173
7.4
PROOF
OF
LEMMAS
7.3.7
AND
7.3.11
.
178
7.5
L
P
ESTIMATES
(REGULAR
COEFFICIENTS)
.
182
7.6
L
P
ESTIMATES
(IRREGULAR
COEFFICIENTS)
.
184
7.7
A
NONLINEAR
EXAMPLE
.
188
7.X
EXERCISES
.
191
8
VARIATIONAL
CRIMES
.
195
8.1
DEPARTURE
FROM
THE
FRAMEWORK
.
196
8.2
FINITE
ELEMENTS
WITH
INTERPOLATED
BOUNDARY
CONDITIONS
.
198
8.3
NONCONFORMING
FINITE
ELEMENTS
.
205
8.4
ISOPARAMETRIC
FINITE
ELEMENTS
.
208
8.X
EXERCISES
.
211
9
APPLICATIONS
TO
PLANAR
ELASTICITY
.
217
9.1
THE
BOUNDARY
VALUE
PROBLEMS
.
217
9.2
WEAK
FORMULATION
AND
KORN
'
S
INEQUALITY
.
219
XII
CONTENTS
9.3
FINITE
ELEMENT
APPROXIMATION
AND
LOCKING
.
226
9.4
A
ROBUST
METHOD
FOR
THE
PURE
DISPLACEMENT
PROBLEM
.
229
9.X
EXERCISES
.
233
10
MIXED
METHODS
.
237
10.1
EXAMPLES
OF
MIXED
VARIATIONAL
FORMULATIONS
.
237
10.2
ABSTRACT
MIXED
FORMULATION
.
239
10.3
DISCRETE
MIXED
FORMULATION
.
242
10.4
CONVERGENCE
RESULTS
FOR
VELOCITY
APPROXIMATION
.
244
10.5
THE
DISCRETE
INF-SUP
CONDITION
.
247
10.6
VERIFICATION
OF
THE
INF-SUP
CONDITION
.
253
10.X
EXERCISES
.
259
11
ITERATIVE
TECHNIQUES
FOR
MIXED
METHODS
.
261
11.1
ITERATED
PENALTY
METHOD
.
261
11.2
STOPPING
CRITERIA
.
265
11.3
AUGMENTED
LAGRANGIAN
METHOD
.
267
11.4
APPLICATION
TO
THE
NAVIER-STOKES
EQUATIONS
.
269
11.5
COMPUTATIONAL
EXAMPLES
.
272
11.X
EXERCISES
.
275
12
APPLICATIONS
OF
OPERATOR-INTERPOLATION
THEORY
.
277
12.1
THE
REAL
METHOD
OF
INTERPOLATION
.
277
12.2
REAL
INTERPOLATION
OF
SOBOLEV
SPACES
.
279
12.3
FINITE
ELEMENT
CONVERGENCE
ESTIMATES
.
282
12.4
THE
SIMULTANEOUS
APPROXIMATION
THEOREM
.
284
12.5
PRECISE
CHARACTERIZATIONS
OF
REGULARITY
.
285
12.X
EXERCISES
.
286
REFERENCES
.
287
INDEX
.
293 |
| any_adam_object | 1 |
| author | Brenner, Susanne C. Scott, L. Ridgway |
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| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)41943049 (DE-599)BVBBV011426673 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 2. print. |
| format | Book |
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| id | DE-604.BV011426673 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:40:46Z |
| institution | BVB |
| isbn | 3540941932 0387941932 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007683459 |
| oclc_num | 41943049 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-824 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-824 DE-11 |
| physical | XII, 297 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Brenner, Susanne C. Verfasser aut The mathematical theory of finite element methods Susanne C. Brenner ; L. Ridgway Scott Corr. 2. print. New York ; Berlin ; Heidelberg Springer 1996 XII, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 15 Literaturverz. S. 287 - 291 Analise numerica larpcal Mathematik Boundary value problems Numerical solutions Finite element method Mathematics Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Scott, L. Ridgway Verfasser (DE-588)124153356 aut Texts in applied mathematics 15 (DE-604)BV002476038 15 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007683459&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brenner, Susanne C. Scott, L. Ridgway The mathematical theory of finite element methods Texts in applied mathematics Analise numerica larpcal Mathematik Boundary value problems Numerical solutions Finite element method Mathematics Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | The mathematical theory of finite element methods |
| title_auth | The mathematical theory of finite element methods |
| title_exact_search | The mathematical theory of finite element methods |
| title_full | The mathematical theory of finite element methods Susanne C. Brenner ; L. Ridgway Scott |
| title_fullStr | The mathematical theory of finite element methods Susanne C. Brenner ; L. Ridgway Scott |
| title_full_unstemmed | The mathematical theory of finite element methods Susanne C. Brenner ; L. Ridgway Scott |
| title_short | The mathematical theory of finite element methods |
| title_sort | the mathematical theory of finite element methods |
| topic | Analise numerica larpcal Mathematik Boundary value problems Numerical solutions Finite element method Mathematics Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Analise numerica Mathematik Boundary value problems Numerical solutions Finite element method Mathematics Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007683459&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
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