Finite elements: theory, fast solvers, and applications in solid mechanics
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Titel laut Haupttitelseite: Finite elements : theory, fast solvers, and applications in elasticity theory |
| Physical Description: | XVII, 365 S. graph. Darst. |
| ISBN: | 0521705185 9780521705189 |
Staff View
MARC
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| 240 | 1 | 0 | |a Finite Elemente |
| 245 | 1 | 0 | |a Finite elements |b theory, fast solvers, and applications in solid mechanics |c Dietrich Braess |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XVII, 365 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Titel laut Haupttitelseite: Finite elements : theory, fast solvers, and applications in elasticity theory | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Elasticity |x Mathematical models | |
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Record in the Search Index
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| adam_text |
Contents
Preface
Preface to the First English Edition
Preface to the German Edition
Notation
Chapter I
Introduction
§ 1.
Examples
— Problems
§2.
Examples
§3.
Discretization
§ 4.
Consistency
vergence theory
Chapter II
Conforming Finite Elements
§ 1.
Introduction to Sobolev spaces
Possible singularities of Hi functions
32 —
§ 2.
Second Order
Variational formulation
ary conditions
boundary conditions
§ 3.
Ellipticity in
ary conditions
boundary conditions
cal consequences of the trace theorem
vi
§ 4.
Model problem
§ 5.
Requirements on the meshes
bility properties
mials
Quadratic rectangular elements
of an element
§ 6.
The Bramble-Hilbert lemma
plete polynomials
verse estimates
the optimality of the estimates
§ 7.
Remarks on regularity
Lj estimates
94 —
§ 8.
Assembling the stiffness matrix
Complexity of setting up the matrix
a grid
Neumann boundary-value problem
Chapter III
Nonconforming and Other Methods
§ 1.
Generalizations of
Crouzeix-Raviart element
boundaries
Problems
§ 2.
Isoparametric triangular elements
elements
§ 3.
Negative norms
tence theorem
of Theorem
§ 4.
Saddle points and minima
Mixed finite element methods
Contents
Saddle point problems with penalty term
141
§5.
The
Thomas element
149 —
norms for the Raviart—Thomas element
haviour of mixed methods
§6.
Variational formulation
incompressible flows
§7.
An
MINI element
ment
§ 8.
Residual estimators
estimators
§ 9.
Chapter IV
The Conjugate Gradient Method
§ 1.
Stationary linear processes
methods
Problems
§2.
The general gradient method
functions
numbers
§ 3.
The
method
unsymmetric matrices
§4.
Preconditioning by SSOR
Remarks on parallelization
lems
viii Contents
§5.
The Uzawa algorithm and its variants
Problems
Chapter V
Multigrid Methods
§ 1.
Smoothing properties of classical iterative methods
grid idea
—
§ 2.
Discrete norms
Approximation property
method
—
§ 3.
A recurrence formula for the W-cycle
the energy norm
—
§4.
Computation of starting values
grid methods with a small number of levels
algorithm
§5.
Schwarz
sequences
Verification of
271
§6.
The multigrid-Newton method
method
Chapter VI
Finite Elements in Solid Mechanics
§ 1.
Kinematics
form
§ 2.
Contents ix
§ 3. Linear
The variational problem
—
method of Hu and Washizu
304 —
remedies
§4.
Plane stress states
ments
§ 5.
The hypotheses
for the Kirchoff plate
§6.
The
the Helmholtz decomposition
model without a Helmholtz decomposition
References
Index |
| adam_txt |
Contents
Preface
Preface to the First English Edition
Preface to the German Edition
Notation
Chapter I
Introduction
§ 1.
Examples
— Problems
§2.
Examples
§3.
Discretization
§ 4.
Consistency
vergence theory
Chapter II
Conforming Finite Elements
§ 1.
Introduction to Sobolev spaces
Possible singularities of Hi functions
32 —
§ 2.
Second Order
Variational formulation
ary conditions
boundary conditions
§ 3.
Ellipticity in
ary conditions
boundary conditions
cal consequences of the trace theorem
vi
§ 4.
Model problem
§ 5.
Requirements on the meshes
bility properties
mials
Quadratic rectangular elements
of an element
§ 6.
The Bramble-Hilbert lemma
plete polynomials
verse estimates
the optimality of the estimates
§ 7.
Remarks on regularity
Lj estimates
94 —
§ 8.
Assembling the stiffness matrix
Complexity of setting up the matrix
a grid
Neumann boundary-value problem
Chapter III
Nonconforming and Other Methods
§ 1.
Generalizations of
Crouzeix-Raviart element
boundaries
Problems
§ 2.
Isoparametric triangular elements
elements
§ 3.
Negative norms
tence theorem
of Theorem
§ 4.
Saddle points and minima
Mixed finite element methods
Contents
Saddle point problems with penalty term
141
§5.
The
Thomas element
149 —
norms for the Raviart—Thomas element
haviour of mixed methods
§6.
Variational formulation
incompressible flows
§7.
An
MINI element
ment
§ 8.
Residual estimators
estimators
§ 9.
Chapter IV
The Conjugate Gradient Method
§ 1.
Stationary linear processes
methods
Problems
§2.
The general gradient method
functions
numbers
§ 3.
The
method
unsymmetric matrices
§4.
Preconditioning by SSOR
Remarks on parallelization
lems
viii Contents
§5.
The Uzawa algorithm and its variants
Problems
Chapter V
Multigrid Methods
§ 1.
Smoothing properties of classical iterative methods
grid idea
—
§ 2.
Discrete norms
Approximation property
method
—
§ 3.
A recurrence formula for the W-cycle
the energy norm
—
§4.
Computation of starting values
grid methods with a small number of levels
algorithm
§5.
Schwarz
sequences
Verification of
271
§6.
The multigrid-Newton method
method
Chapter VI
Finite Elements in Solid Mechanics
§ 1.
Kinematics
form
§ 2.
Contents ix
§ 3. Linear
The variational problem
—
method of Hu and Washizu
304 —
remedies
§4.
Plane stress states
ments
§ 5.
The hypotheses
for the Kirchoff plate
§6.
The
the Helmholtz decomposition
model without a Helmholtz decomposition
References
Index |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Braess, Dietrich 1938- |
| author_GND | (DE-588)106060325 |
| author_facet | Braess, Dietrich 1938- |
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| classification_rvk | SK 910 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)233787102 (DE-599)BVBBV022395513 |
| dewey-full | 620.00151535 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.00151535 |
| dewey-search | 620.00151535 |
| dewey-sort | 3620.00151535 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
| format | Book |
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| index_date | 2024-07-02T17:16:24Z |
| indexdate | 2024-09-12T00:07:23Z |
| institution | BVB |
| isbn | 0521705185 9780521705189 |
| language | English German |
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| spelling | Braess, Dietrich 1938- Verfasser (DE-588)106060325 aut Finite Elemente Finite elements theory, fast solvers, and applications in solid mechanics Dietrich Braess 3. ed. Cambridge [u.a.] Cambridge Univ. Press 2007 XVII, 365 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Titel laut Haupttitelseite: Finite elements : theory, fast solvers, and applications in elasticity theory Mathematisches Modell Elasticity Mathematical models Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015604261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Braess, Dietrich 1938- Finite elements theory, fast solvers, and applications in solid mechanics Mathematisches Modell Elasticity Mathematical models Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4123623-3 |
| title | Finite elements theory, fast solvers, and applications in solid mechanics |
| title_alt | Finite Elemente |
| title_auth | Finite elements theory, fast solvers, and applications in solid mechanics |
| title_exact_search | Finite elements theory, fast solvers, and applications in solid mechanics |
| title_exact_search_txtP | Finite elements theory, fast solvers, and applications in solid mechanics |
| title_full | Finite elements theory, fast solvers, and applications in solid mechanics Dietrich Braess |
| title_fullStr | Finite elements theory, fast solvers, and applications in solid mechanics Dietrich Braess |
| title_full_unstemmed | Finite elements theory, fast solvers, and applications in solid mechanics Dietrich Braess |
| title_short | Finite elements |
| title_sort | finite elements theory fast solvers and applications in solid mechanics |
| title_sub | theory, fast solvers, and applications in solid mechanics |
| topic | Mathematisches Modell Elasticity Mathematical models Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Mathematisches Modell Elasticity Mathematical models Finite element method Finite-Elemente-Methode Lehrbuch |
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