Numerical treatment of partial differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English German |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. [571] - 583 |
| Physical Description: | XII, 591 S. graph. Darst. |
| ISBN: | 9783540715825 |
Staff View
MARC
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| 020 | |a 9783540715825 |9 978-3-540-71582-5 | ||
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| 100 | 1 | |a Großmann, Christian |d 1946- |e Verfasser |0 (DE-588)124824269 |4 aut | |
| 240 | 1 | 0 | |a Numerische Behandlung partieller Differentialgleichungen |
| 245 | 1 | 0 | |a Numerical treatment of partial differential equations |c Christian Grossmann ; Hans-Görg Roos. Transl. and rev. by Martin Stynes |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XII, 591 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 500 | |a Literaturverz. S. [571] - 583 | ||
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Différences finies | |
| 650 | 4 | |a Éléments finis, Méthode des | |
| 650 | 4 | |a Équations aux dérivées partielles - Solutions numériques | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Finite differences | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Roos, Hans-Görg |d 1949- |e Verfasser |0 (DE-588)108923479 |4 aut | |
| 700 | 1 | |a Stynes, Martin |d 1951- |0 (DE-588)114088942 |4 trl | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016137110 | ||
Record in the Search Index
| _version_ | 1804137164640878592 |
|---|---|
| adam_text | Contents
Notation.......................................................
XI
1 Basics ..................................................... 1
1.1
Classification
and Correctness
............................. 1
1.2
Fourier s Method, Integral Transforms
..................... 5
1.3
Maximum Principle, Fundamental Solution
................. 9
1.3.1
Elliptic Boundary Value Problems
................... 9
1.3.2
Parabolic Equations and Initial-Boundary Value
Problems
......................................... 15
1.3.3
Hyperbolic Initial and Initial-Boundary Value Problems
18
2
Finite Difference Methods
................................. 23
2.1
Basic Concepts
.......................................... 23
2.2
Illustrative Examples
.................................... 31
2.3
Transportation Problems and Conservation Laws
............ 36
2.3.1
The One-Dimensional Linear Case
................... 37
2.3.2
Properties of Nonlinear Conservation Laws
........... 48
2.3.3
Difference Methods for Nonlinear Conservation Laws
... 53
2.4
Elliptic Boundary Value Problems
......................... 61
2.4.1
Elliptic Boundary Value Problems
................... 61
2.4.2
The Classical Approach to Finite Difference Methods
. . 62
2.4.3
Discrete Green s Function
.......................... 74
2.4.4
Difference Stencils and Discretization in General
Domains
......................................... 76
2.4.5
Mixed Derivatives, Fourth Order Operators
........... 82
2.4.6
Local Grid Refinements
........................... 89
2.5
Finite Volume Methods as Finite Difference Schemes
......... 90
2.6
Parabolic Initial-Boundary Value Problems
................. 103
2.6.1
Problems in One Space Dimension
................... 104
2.6.2
Problems in Higher Space Dimensions
................ 109
2.6.3
Semi-Discretization
................................ 113
VIII Contents
2.7
Second-Order Hyperbolic Problems
........................118
3
Weak Solutions
............................................125
3.1
Introduction
............................................125
3.2
Adapted Function Spaces
.................................128
3.3
Variational Equations and Conforming Approximation
.......142
3.4
Weakening V-ellipticity
..................................163
3.5
Nonlinear Problems
......................................167
4
The Finite Element Method
...............................173
4.1
A First Example
........................................173
4.2
Finite-Element-Spaces
...................................178
4.2.1
Local and Global Properties
........................178
4.2.2
Examples of Finite Element Spaces in K2 and R3
......189
4.3
Practical Aspects of the Finite Element Method
.............202
4.3.1
Structure of a Finite Element Code
..................202
4.3.2
Description of the Problem
.........................203
4.3.3
Generation of the Discrete Problem
..................205
4.3.4
Mesh Generation and Manipulation
..................210
4.4
Convergence of Conforming Methods
.......................217
4.4.1
Interpolation and Projection Error in Sobolev Spaces
. . 217
4.4.2
Hubert Space Error Estimates
......................227
4.4.3
Inverse Inequalities and Pointwise Error Estimates
.....232
4.5
Nonconforming Finite Element Methods
....................238
4.5.1
Introduction
......................................238
4.5.2 Ansatz
Spaces with Low Smoothness
................239
4.5.3
Numerical Integration
..............................244
4.5.4
The Finite Volume Method Analysed from a Finite
Element Viewpoint
................................251
4.5.5
Remarks on Curved Boundaries
.....................254
4.6
Mixed Finite Elements
...................................258
4.6.1
Mixed Variational Equations and Saddle Points
.......258
4.6.2
Conforming Approximation of Mixed Variational
Equations
........................................265
4.6.3
Weaker Regularity for the
Poisson
and Biharmonic
Equations
........................................272
4.6.4
Penalty Methods and Modified
Lagrange
Functions
.... 277
4.7
Error Estimators and Adaptive
FEM
......................287
4.7.1
The Residual Error Estimator
.......................288
4.7.2
Averaging and Goal-Oriented Estimators
.............292
4.8
The Discontinuous Galerkin Method
.......................294
4.8.1
The Primal Formulation for a Reaction-Diffusion
Problem
..........................................295
4.8.2
First-Order Hyperbolic Problems
....................299
4.8.3
Error Estimates for a Convection-Diffusion Problem
. . . 302
Contents
IX
4.9
Further Aspects of the Finite Element Method
..............306
4.9.1
Conditioning of the Stiffness Matrix
.................306
4.9.2
Eigenvalue Problems
...............................307
4.9.3
Superconvergence
.................................310
4.9.4
ρ-
and hp-Versions
................................314
Finite Element Methods for Unsteady Problems
...........317
5.1
Parabolic Problems
......................................317
5.1.1
On the Weak Formulation
..........................317
5.1.2
Semi-Discretization by Finite Elements
...............321
5.1.3
Temporal Discretization by Standard Methods
........330
5.1.4
Temporal Discretization with Discontinuous Galerkin
Methods
.........................................337
5.1.5
Rothe s Method
...................................343
5.1.6
Error Control
.....................................347
5.2
Second-Order Hyperbolic Problems
........................356
5.2.1
Weak Formulation of the Problem
...................356
5.2.2
Semi-Discretization by Finite Elements
...............358
5.2.3
Temporal Discretization
............................363
5.2.4
Rothe s Method for Hyperbolic Problems
.............368
5.2.5
Remarks on Error Control
..........................372
Singularly Perturbed Boundary Value Problems
...........375
6.1
Two-Point Boundary Value Problems
......................376
6.1.1
Analytical Behaviour of the Solution
.................376
6.1.2
Discretization on Standard Meshes
..................383
6.1.3
Layer-adapted Meshes
.............................394
6.2
Parabolic Problems, One-dimensional in Space
..............399
6.2.1
The Analytical Behaviour of the Solution
.............399
6.2.2
Discretization
.....................................401
6.3
Convection-Diffusion Problems in Several Dimensions
........406
6.3.1
Analysis of Elliptic Convection-Diffusion Problems
.....406
6.3.2
Discretization on Standard Meshes
..................412
6.3.3
Layer-adapted Meshes
.............................427
6.3.4
Parabolic Problems, Higher-Dimensional in Space
.....430
Variational Inequalities, Optimal Control
..................435
7.1
Analytic Properties
......................................435
7.2
Discretization of Variational Inequalities
....................447
7.3
Penalty Methods
........................................457
7.3.1
Basic Concept of Penalty Methods
...................457
7.3.2
Adjustment of Penalty and Discretization Parameters
. . 473
7.4
Optimal Control of PDEs
.................................480
7.4.1
Analysis of an Elliptic Model Problem
...............480
7.4.2
Discretization by Finite Element Methods
............489
X
Contents
8
Numerical Methods for Discretized Problems
..............499
8.1
Some Particular Properties of the Problems
.................499
8.2
Direct Methods
.........................................502
8.2.1
Gaussian Elimination for Banded Matrices
............502
8.2.2
Fast Solution of Discrete
Poisson
Equations. FFT
.....504
8.3
Classical Iterative Methods
...............................510
8.3.1
Basic Structure and Convergence
....................510
8.3.2
Jacobi and Gauss-Seidel Methods
...................514
8.3.3
Block Iterative Methods
............................520
8.3.4
Relaxation and Splitting Methods
...................524
8.4
The Conjugate Gradient Method
..........................530
8.4.1
The Basic Idea, Convergence Properties
..............530
8.4.2
Preconditioned
CG
Methods
........................538
8.5
Multigrid Methods
......................................548
8.6
Domain Decomposition. Parallel Algorithms
................560
Bibliography: Textbooks and Monographs
.....................571
Bibliography: Original Papers
.................................577
Index
..........................................................585
Universitext
CHRISTIAN GROSSMANN,
born in
1946,
is
Professor
of Numerical Analysis at
the
TU
Dresden. He works
mainly in numerical methods
for optimization problems
and for discretization of
differential equations.
HANS-GÖRG
ROOS,
born in
1949,
is Professor of
Numerical Mathematics
at the
TU
Dresden. He works
mainly in numerical methods
for singularly perturbed
differential equations.
MARTIN STYNES,
born in 1951,1s a Mathematics
Department Professor at the
National University of Ireland,
Cork. He works mainly on
numerical methods for
singularly perturbed differen¬
tial equations.
Numerical Treatment of Partial Differential Equations
This book deals with discretization techniques for elliptic, parabolic and
hyperbolic partial differential equations. It provides an introduction to the
main principles of discretizations and presents to the reader the ideas and
analysis of advanced numerical methods in this area.
It is the authors aim to give mathematically-inclined students, scientists
and engineers a textbook that contains all the basic discretization techniques
for the three fundamental types of partial differential equations and in which
the reader can find analytical tools, properties of discretizations, and some
advice on algorithmic aspects. The book also covers recent research develop¬
ments: for instance, introductions are given to a posteriori error estimation,
discontinuous Galerkin methods, and optimal control for partial differential
equations
-
these topics of current interest are rarely considered in other
textbooks. While
fìnite
element methods are the main focus of the book,
fìnite
difference methods and
fìnite
volume techniques are also presented.
Furthermore, the book provides the basic tools needed to solve the discrete
problems generated, while chapters on singularly perturbed problems,
variational inequalities and optimal control illuminate special topics that
reflect the research interests of the authors.
ISBN
978-3-540-71582-5
9 783540 715825
sorinaer.o
|
| adam_txt |
Contents
Notation.
XI
1 Basics . 1
1.1
Classification
and Correctness
. 1
1.2
Fourier' s Method, Integral Transforms
. 5
1.3
Maximum Principle, Fundamental Solution
. 9
1.3.1
Elliptic Boundary Value Problems
. 9
1.3.2
Parabolic Equations and Initial-Boundary Value
Problems
. 15
1.3.3
Hyperbolic Initial and Initial-Boundary Value Problems
18
2
Finite Difference Methods
. 23
2.1
Basic Concepts
. 23
2.2
Illustrative Examples
. 31
2.3
Transportation Problems and Conservation Laws
. 36
2.3.1
The One-Dimensional Linear Case
. 37
2.3.2
Properties of Nonlinear Conservation Laws
. 48
2.3.3
Difference Methods for Nonlinear Conservation Laws
. 53
2.4
Elliptic Boundary Value Problems
. 61
2.4.1
Elliptic Boundary Value Problems
. 61
2.4.2
The Classical Approach to Finite Difference Methods
. . 62
2.4.3
Discrete Green's Function
. 74
2.4.4
Difference Stencils and Discretization in General
Domains
. 76
2.4.5
Mixed Derivatives, Fourth Order Operators
. 82
2.4.6
Local Grid Refinements
. 89
2.5
Finite Volume Methods as Finite Difference Schemes
. 90
2.6
Parabolic Initial-Boundary Value Problems
. 103
2.6.1
Problems in One Space Dimension
. 104
2.6.2
Problems in Higher Space Dimensions
. 109
2.6.3
Semi-Discretization
. 113
VIII Contents
2.7
Second-Order Hyperbolic Problems
.118
3
Weak Solutions
.125
3.1
Introduction
.125
3.2
Adapted Function Spaces
.128
3.3
Variational Equations and Conforming Approximation
.142
3.4
Weakening V-ellipticity
.163
3.5
Nonlinear Problems
.167
4
The Finite Element Method
.173
4.1
A First Example
.173
4.2
Finite-Element-Spaces
.178
4.2.1
Local and Global Properties
.178
4.2.2
Examples of Finite Element Spaces in K2 and R3
.189
4.3
Practical Aspects of the Finite Element Method
.202
4.3.1
Structure of a Finite Element Code
.202
4.3.2
Description of the Problem
.203
4.3.3
Generation of the Discrete Problem
.205
4.3.4
Mesh Generation and Manipulation
.210
4.4
Convergence of Conforming Methods
.217
4.4.1
Interpolation and Projection Error in Sobolev Spaces
. . 217
4.4.2
Hubert Space Error Estimates
.227
4.4.3
Inverse Inequalities and Pointwise Error Estimates
.232
4.5
Nonconforming Finite Element Methods
.238
4.5.1
Introduction
.238
4.5.2 Ansatz
Spaces with Low Smoothness
.239
4.5.3
Numerical Integration
.244
4.5.4
The Finite Volume Method Analysed from a Finite
Element Viewpoint
.251
4.5.5
Remarks on Curved Boundaries
.254
4.6
Mixed Finite Elements
.258
4.6.1
Mixed Variational Equations and Saddle Points
.258
4.6.2
Conforming Approximation of Mixed Variational
Equations
.265
4.6.3
Weaker Regularity for the
Poisson
and Biharmonic
Equations
.272
4.6.4
Penalty Methods and Modified
Lagrange
Functions
. 277
4.7
Error Estimators and Adaptive
FEM
.287
4.7.1
The Residual Error Estimator
.288
4.7.2
Averaging and Goal-Oriented Estimators
.292
4.8
The Discontinuous Galerkin Method
.294
4.8.1
The Primal Formulation for a Reaction-Diffusion
Problem
.295
4.8.2
First-Order Hyperbolic Problems
.299
4.8.3
Error Estimates for a Convection-Diffusion Problem
. . . 302
Contents
IX
4.9
Further Aspects of the Finite Element Method
.306
4.9.1
Conditioning of the Stiffness Matrix
.306
4.9.2
Eigenvalue Problems
.307
4.9.3
Superconvergence
.310
4.9.4
ρ-
and hp-Versions
.314
Finite Element Methods for Unsteady Problems
.317
5.1
Parabolic Problems
.317
5.1.1
On the Weak Formulation
.317
5.1.2
Semi-Discretization by Finite Elements
.321
5.1.3
Temporal Discretization by Standard Methods
.330
5.1.4
Temporal Discretization with Discontinuous Galerkin
Methods
.337
5.1.5
Rothe's Method
.343
5.1.6
Error Control
.347
5.2
Second-Order Hyperbolic Problems
.356
5.2.1
Weak Formulation of the Problem
.356
5.2.2
Semi-Discretization by Finite Elements
.358
5.2.3
Temporal Discretization
.363
5.2.4
Rothe's Method for Hyperbolic Problems
.368
5.2.5
Remarks on Error Control
.372
Singularly Perturbed Boundary Value Problems
.375
6.1
Two-Point Boundary Value Problems
.376
6.1.1
Analytical Behaviour of the Solution
.376
6.1.2
Discretization on Standard Meshes
.383
6.1.3
Layer-adapted Meshes
.394
6.2
Parabolic Problems, One-dimensional in Space
.399
6.2.1
The Analytical Behaviour of the Solution
.399
6.2.2
Discretization
.401
6.3
Convection-Diffusion Problems in Several Dimensions
.406
6.3.1
Analysis of Elliptic Convection-Diffusion Problems
.406
6.3.2
Discretization on Standard Meshes
.412
6.3.3
Layer-adapted Meshes
.427
6.3.4
Parabolic Problems, Higher-Dimensional in Space
.430
Variational Inequalities, Optimal Control
.435
7.1
Analytic Properties
.435
7.2
Discretization of Variational Inequalities
.447
7.3
Penalty Methods
.457
7.3.1
Basic Concept of Penalty Methods
.457
7.3.2
Adjustment of Penalty and Discretization Parameters
. . 473
7.4
Optimal Control of PDEs
.480
7.4.1
Analysis of an Elliptic Model Problem
.480
7.4.2
Discretization by Finite Element Methods
.489
X
Contents
8
Numerical Methods for Discretized Problems
.499
8.1
Some Particular Properties of the Problems
.499
8.2
Direct Methods
.502
8.2.1
Gaussian Elimination for Banded Matrices
.502
8.2.2
Fast Solution of Discrete
Poisson
Equations. FFT
.504
8.3
Classical Iterative Methods
.510
8.3.1
Basic Structure and Convergence
.510
8.3.2
Jacobi and Gauss-Seidel Methods
.514
8.3.3
Block Iterative Methods
.520
8.3.4
Relaxation and Splitting Methods
.524
8.4
The Conjugate Gradient Method
.530
8.4.1
The Basic Idea, Convergence Properties
.530
8.4.2
Preconditioned
CG
Methods
.538
8.5
Multigrid Methods
.548
8.6
Domain Decomposition. Parallel Algorithms
.560
Bibliography: Textbooks and Monographs
.571
Bibliography: Original Papers
.577
Index
.585
Universitext
CHRISTIAN GROSSMANN,
born in
1946,
is
Professor
of Numerical Analysis at
the
TU
Dresden. He works
mainly in numerical methods
for optimization problems
and for discretization of
differential equations.
HANS-GÖRG
ROOS,
born in
1949,
is Professor of
Numerical Mathematics
at the
TU
Dresden. He works
mainly in numerical methods
for singularly perturbed
differential equations.
MARTIN STYNES,
born in 1951,1s a Mathematics
Department Professor at the
National University of Ireland,
Cork. He works mainly on
numerical methods for
singularly perturbed differen¬
tial equations.
Numerical Treatment of Partial Differential Equations
This book deals with discretization techniques for elliptic, parabolic and
hyperbolic partial differential equations. It provides an introduction to the
main principles of discretizations and presents to the reader the ideas and
analysis of advanced numerical methods in this area.
It is the authors' aim to give mathematically-inclined students, scientists
and engineers a textbook that contains all the basic discretization techniques
for the three fundamental types of partial differential equations and in which
the reader can find analytical tools, properties of discretizations, and some
advice on algorithmic aspects. The book also covers recent research develop¬
ments: for instance, introductions are given to a posteriori error estimation,
discontinuous Galerkin methods, and optimal control for partial differential
equations
-
these topics of current interest are rarely considered in other
textbooks. While
fìnite
element methods are the main focus of the book,
fìnite
difference methods and
fìnite
volume techniques are also presented.
Furthermore, the book provides the basic tools needed to solve the discrete
problems generated, while chapters on singularly perturbed problems,
variational inequalities and optimal control illuminate special topics that
reflect the research interests of the authors.
ISBN
978-3-540-71582-5
9 783540 715825
sorinaer.o |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Großmann, Christian 1946- Roos, Hans-Görg 1949- |
| author2 | Stynes, Martin 1951- |
| author2_role | trl |
| author2_variant | m s ms |
| author_GND | (DE-588)124824269 (DE-588)108923479 (DE-588)114088942 |
| author_facet | Großmann, Christian 1946- Roos, Hans-Görg 1949- Stynes, Martin 1951- |
| author_role | aut aut |
| author_sort | Großmann, Christian 1946- |
| author_variant | c g cg h g r hgr |
| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)185096377 (DE-599)BVBBV022932307 |
| dewey-full | 518/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.64 |
| dewey-search | 518/.64 |
| dewey-sort | 3518 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV022932307 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:55:02Z |
| indexdate | 2024-07-09T21:07:57Z |
| institution | BVB |
| isbn | 9783540715825 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016137110 |
| oclc_num | 185096377 |
| open_access_boolean | |
| owner | DE-824 DE-29T DE-83 DE-20 DE-703 DE-11 |
| owner_facet | DE-824 DE-29T DE-83 DE-20 DE-703 DE-11 |
| physical | XII, 591 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Großmann, Christian 1946- Verfasser (DE-588)124824269 aut Numerische Behandlung partieller Differentialgleichungen Numerical treatment of partial differential equations Christian Grossmann ; Hans-Görg Roos. Transl. and rev. by Martin Stynes Berlin [u.a.] Springer 2007 XII, 591 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. [571] - 583 Analyse numérique Différences finies Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Finite differences Finite element method Numerical analysis Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Roos, Hans-Görg 1949- Verfasser (DE-588)108923479 aut Stynes, Martin 1951- (DE-588)114088942 trl Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016137110&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016137110&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Großmann, Christian 1946- Roos, Hans-Görg 1949- Numerical treatment of partial differential equations Analyse numérique Différences finies Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Finite differences Finite element method Numerical analysis Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4128130-5 |
| title | Numerical treatment of partial differential equations |
| title_alt | Numerische Behandlung partieller Differentialgleichungen |
| title_auth | Numerical treatment of partial differential equations |
| title_exact_search | Numerical treatment of partial differential equations |
| title_exact_search_txtP | Numerical treatment of partial differential equations |
| title_full | Numerical treatment of partial differential equations Christian Grossmann ; Hans-Görg Roos. Transl. and rev. by Martin Stynes |
| title_fullStr | Numerical treatment of partial differential equations Christian Grossmann ; Hans-Görg Roos. Transl. and rev. by Martin Stynes |
| title_full_unstemmed | Numerical treatment of partial differential equations Christian Grossmann ; Hans-Görg Roos. Transl. and rev. by Martin Stynes |
| title_short | Numerical treatment of partial differential equations |
| title_sort | numerical treatment of partial differential equations |
| topic | Analyse numérique Différences finies Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Finite differences Finite element method Numerical analysis Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Analyse numérique Différences finies Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Finite differences Finite element method Numerical analysis Partielle Differentialgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016137110&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016137110&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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