Robust numerical methods for singularly perturbed differential equations: convection-diffusion-reaction and flow problems
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| Previous Title: | Numerical methods for singularly perturbed differential equations |
|---|---|
| Main Authors: | , , |
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | 2. ed. |
| Series: | Springer series in computational mathematics
24 |
| Subjects: | |
| Online Access: | Kapitel 2 Kapitel 3 Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XIV, 604 S. graph. Darst. |
| ISBN: | 9783540344667 9783540344674 |
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MARC
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| 100 | 1 | |a Roos, Hans-Görg |d 1949- |e Verfasser |0 (DE-588)108923479 |4 aut | |
| 245 | 1 | 0 | |a Robust numerical methods for singularly perturbed differential equations |b convection-diffusion-reaction and flow problems |c Hans-Görg Roos ; Martin Stynes ; Lutz Tobiska |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIV, 604 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in computational mathematics |v 24 | |
| 650 | 4 | |a Perturbations singulières (Mathématiques) | |
| 650 | 4 | |a Équations différentielles - Solutions numériques | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Singular perturbations (Mathematics) | |
| 650 | 0 | 7 | |a Singuläre Störung |0 (DE-588)4055100-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Tobiska, Lutz |d 1950- |e Verfasser |0 (DE-588)109576454 |4 aut | |
| 780 | 0 | 0 | |i 1. Auflage |t Numerical methods for singularly perturbed differential equations |w (DE-604)BV010616603 |
| 830 | 0 | |a Springer series in computational mathematics |v 24 |w (DE-604)BV000012004 |9 24 | |
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| _version_ | 1804138046223810560 |
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| adam_text | Contents
Notation......................................................XIII
Introduction
................................................... 1
Part I Ordinary Differential Equations
1
The Analytical Behaviour of Solutions
..................... 9
1.1
Linear Second-Order Problems Without Turning Points
...... 11
1.1.1
Asymptotic Expansions
............................ 12
1.1.2
The Green s Function and Stability Estimates
......... 16
1.1.3
A Priori Estimates for Derivatives and Solution
Decomposition
.................................... 21
1.2
Linear Second-Order Turning-Point Problems
............... 25
1.3 Quasilinear
Problems
.................................... 29
1.4
Linear Higher-Order Problems and Systems
................. 35
1.4.1
Asymptotic Expansions for Higher-Order Problems
.... 35
1.4.2
A Stability Result
................................. 36
1.4.3
Systems of Ordinary Differential Equations
........... 38
2
Numerical Methods for Second-Order Boundary Value
Problems
.................................................. 41
2.1
Finite Difference Methods on Equidistant Meshes
............ 41
2.1.1
Classical Convergence Theory for Central
Differencing
...................................... 41
2.1.2
Upwind Schemes
.................................. 45
2.1.3
The Concept of Uniform Convergence
................ 57
2.1.4
Uniformly Convergent Schemes of Higher Order
....... 66
2.1.5
Linear Turning-Point Problems
...................... 68
2.1.6
Some Nonlinear Problems
.......................... 71
2.2
Finite Element Methods on Standard Meshes
............... 76
2.2.1
Basic Results for Standard Finite Element Methods
.... 76
VIII Contents
2.2.2
Upwind Finite Elements
............................ 79
2.2.3
Stabilized Higher-Order Methods
.................... 84
2.2.4
Variational Multiscale and Differentiated Residual
Methods
......................................... 95
2.2.5
Uniformly Convergent Finite Element Methods
........104
2.3
Finite Volume Methods
..................................114
2.4
Finite Difference Methods on Layer-adapted Grids
...........116
2.4.1
Graded Meshes
...................................119
2.4.2
Piecewise Equidistant Meshes
.......................127
2.5
Adaptive Strategies Based on Finite Differences
.............141
Part II Parabolic Initial-Boundary Value Problems in One Space
Dimension
1
Introduction
...............................................155
2
Analytical Behaviour of Solutions
..........................159
2.1
Existence, Uniqueness, Comparison Principle
...............159
2.2
Asymptotic Expansions and Bounds on Derivatives
..........161
3
Finite Difference Methods
.................................169
3.1
First-Order Problems
....................................169
3.1.1
Consistency
......................................169
3.1.2
Stability
.........................................171
3.1.3
Convergence in
¿2.................................174
3.2
Convection-Diffusion Problems
............................177
3.2.1
Consistency and Stability
..........................178
3.2.2
Convergence
......................................182
3.3
Polynomial Schemes
.....................................183
3.4
Uniformly Convergent Methods
...........................187
3.4.1
Exponential Fitting in Space
........................188
3.4.2
Layer-Adapted Tensor-Product Meshes
...............189
3.4.3
Reaction-Diffusion Problems
........................191
4
Finite Element Methods
...................................195
4.1
Space-Based Methods
....................................196
4.1.1
Polynomial Upwinding
.............................197
4.1.2
Uniformly Convergent Schemes
......................199
4.1.3
Local Error Estimates
.............................203
4.2
Subcharacteristic-Based Methods
..........................205
4.2.1
SDFEM in Space-Time
.............................206
4.2.2
Explicit Gaierkin Methods
..........................211
4.2.3
Eulerian-Lagrangian Methods
.......................217
Contents
IX
Two Adaptive Methods
....................................223
5.1
Streamline Diffusion Methods
.............................223
5.2
Moving Mesh Methods (r-refinement)
......................225
Part III Elliptic and Parabolic Problems in Several Space
Dimensions
1
Analytical Behaviour of Solutions
..........................235
1.1
Classical and Weak Solutions
.............................235
1.2
The Reduced Problem
...................................238
1.3
Asymptotic Expansions and Boundary Layers
...............243
1.4
A Priori Estimates and Solution Decomposition
.............247
2
Finite Difference Methods
.................................259
2.1
Finite Difference Methods on Standard Meshes
..............259
2.1.1
Exponential Boundary Layers
.......................259
2.1.2
Parabolic Boundary Layers
.........................266
2.2
Layer-Adapted Meshes
...................................268
2.2.1
Exponential Boundary Layers
.......................268
2.2.2
Parabolic Layers
..................................274
3
Finite Element Methods
...................................277
3.1
Inverse-Monotonicity-Preserving Methods Based on Finite
Volume Ideas
...........................................278
3.2
Residual-Based Stabilizations
.............................302
3.2.1
Streamline Diffusion Finite Element Method
(SDFEM)
........................................302
3.2.2
Galerkin Least Squares Finite Element Method
(GLSFEM)
.......................................327
3.2.3
Residual-Free Bubbles
.............................333
3.3
Adding Symmetric Stabilizing Terms
.......................338
3.3.1
Local Projection Stabilization
.......................338
3.3.2
Continuous Interior Penalty Stabilization
.............352
3.4
The Discontinuous Galerkin Finite Element Method
.........363
3.4.1
The Primal Formulation for a Reaction-Diffusion
Problem
..........................................363
3.4.2
A First-Order Hyperbolic Problem
..................368
3.4.3
dGFEM Error Analysis for Convection-Diffusion
Problems
.........................................371
3.5
Uniformly Convergent Methods
...........................376
3.5.1
Operator-Fitted Methods
...........................377
3.5.2
Layer-Adapted Meshes
.............................381
3.6
Adaptive Methods
.......................................407
3.6.1
Adaptive Finite Element Methods for Non-Singularly
Perturbed Elliptic Problems: an Introduction
.........407
X
Contents
3.6.2 Robust
and Semi-Robust Residual Type Error
Estimators
.......................................414
3.6.3
A Variant of the DWR Method for Streamline
Diffusion
.........................................421
4
Time-Dependent Problems
................................427
4.1
Analytical Behaviour of Solutions
..........................428
4.2
Finite Difference Methods
................................429
4.3
Finite Element Methods
..................................434
Part IV The Incompressible Navier-Stokes Equations
1
Existence and Uniqueness Results
.........................449
2
Upwind Finite Element Method
...........................453
3
Higher-Order Methods of Streamline Diffusion Type
......465
3.1
The
Oseen
Problem
......................................466
3.2
The Navier-Stokes Problem
...............................476
4
Local Projection Stabilization for Equal-Order
Interpolation
..............................................485
4.1
Local Projection Stabilization in an Abstract Setting
.........486
4.2
Convergence Analysis
....................................488
4.2.1
The Special
Interpolant
............................488
4.2.2
Stability
.........................................489
4.2.3
Consistency Error
.................................491
4.2.4
A priori Error Estimate
............................492
4.3
Local Projection onto Coarse-Mesh Spaces
..................498
4.3.1
Simplices
.........................................498
4.3.2
Quadrilaterals and Hexahedra
.......................499
4.4
Schemes Based on Enrichment of Approximation Spaces
......501
4.4.1
Simplices
.........................................502
4.4.2
Quadrilaterals and Hexahedra
.......................502
4.5
Relationship to Subgrid Modelling
.........................504
4.5.1
Two-Level Approach with Piecewise Linear Elements
.. 505
4.5.2
Enriched Piecewise Linear Elements
.................507
4.5.3
Spectral Equivalence of the Stabilizing Terms on
Simplices
.........................................508
5
Local Projection Method for Inf-Sup Stable Elements
.....511
5.1
Discretization by Inf-Sup Stable Elements
..................512
5.2
Stability and Consistency
.................................514
5.3
Convergence
............................................516
5.3.1
Methods of Order
r
in the Case
σ
> 0................517
5.3.2
Methods of Order
r
in the Case
σ
> 0................522
5.3.3
Methods of Order
r
+ 1/2..........................526
Contents
XI
6
Mass Conservation for Coupled Flow-Transport
Problems
..................................................529
6.1
A Model Problem
.......................................529
6.2
Continuous and Discrete Mass Conservation
................530
6.3
Approximated Incompressible Flows
.......................532
6.4
Mass-Conservative Methods
...............................534
6.4.1
Higher-Order Flow Approximation
...................534
6.4.2
Post-Processing of the Discrete Velocity
..............536
6.4.3
Scott-Vogelius Elements
............................542
7
Adaptive Error Control
....................................545
References
.....................................................551
Index
..........................................................599
|
| adam_txt |
Contents
Notation.XIII
Introduction
. 1
Part I Ordinary Differential Equations
1
The Analytical Behaviour of Solutions
. 9
1.1
Linear Second-Order Problems Without Turning Points
. 11
1.1.1
Asymptotic Expansions
. 12
1.1.2
The Green's Function and Stability Estimates
. 16
1.1.3
A Priori Estimates for Derivatives and Solution
Decomposition
. 21
1.2
Linear Second-Order Turning-Point Problems
. 25
1.3 Quasilinear
Problems
. 29
1.4
Linear Higher-Order Problems and Systems
. 35
1.4.1
Asymptotic Expansions for Higher-Order Problems
. 35
1.4.2
A Stability Result
. 36
1.4.3
Systems of Ordinary Differential Equations
. 38
2
Numerical Methods for Second-Order Boundary Value
Problems
. 41
2.1
Finite Difference Methods on Equidistant Meshes
. 41
2.1.1
Classical Convergence Theory for Central
Differencing
. 41
2.1.2
Upwind Schemes
. 45
2.1.3
The Concept of Uniform Convergence
. 57
2.1.4
Uniformly Convergent Schemes of Higher Order
. 66
2.1.5
Linear Turning-Point Problems
. 68
2.1.6
Some Nonlinear Problems
. 71
2.2
Finite Element Methods on Standard Meshes
. 76
2.2.1
Basic Results for Standard Finite Element Methods
. 76
VIII Contents
2.2.2
Upwind Finite Elements
. 79
2.2.3
Stabilized Higher-Order Methods
. 84
2.2.4
Variational Multiscale and Differentiated Residual
Methods
. 95
2.2.5
Uniformly Convergent Finite Element Methods
.104
2.3
Finite Volume Methods
.114
2.4
Finite Difference Methods on Layer-adapted Grids
.116
2.4.1
Graded Meshes
.119
2.4.2
Piecewise Equidistant Meshes
.127
2.5
Adaptive Strategies Based on Finite Differences
.141
Part II Parabolic Initial-Boundary Value Problems in One Space
Dimension
1
Introduction
.155
2
Analytical Behaviour of Solutions
.159
2.1
Existence, Uniqueness, Comparison Principle
.159
2.2
Asymptotic Expansions and Bounds on Derivatives
.161
3
Finite Difference Methods
.169
3.1
First-Order Problems
.169
3.1.1
Consistency
.169
3.1.2
Stability
.171
3.1.3
Convergence in
¿2.174
3.2
Convection-Diffusion Problems
.177
3.2.1
Consistency and Stability
.178
3.2.2
Convergence
.182
3.3
Polynomial Schemes
.183
3.4
Uniformly Convergent Methods
.187
3.4.1
Exponential Fitting in Space
.188
3.4.2
Layer-Adapted Tensor-Product Meshes
.189
3.4.3
Reaction-Diffusion Problems
.191
4
Finite Element Methods
.195
4.1
Space-Based Methods
.196
4.1.1
Polynomial Upwinding
.197
4.1.2
Uniformly Convergent Schemes
.199
4.1.3
Local Error Estimates
.203
4.2
Subcharacteristic-Based Methods
.205
4.2.1
SDFEM in Space-Time
.206
4.2.2
Explicit Gaierkin Methods
.211
4.2.3
Eulerian-Lagrangian Methods
.217
Contents
IX
Two Adaptive Methods
.223
5.1
Streamline Diffusion Methods
.223
5.2
Moving Mesh Methods (r-refinement)
.225
Part III Elliptic and Parabolic Problems in Several Space
Dimensions
1
Analytical Behaviour of Solutions
.235
1.1
Classical and Weak Solutions
.235
1.2
The Reduced Problem
.238
1.3
Asymptotic Expansions and Boundary Layers
.243
1.4
A Priori Estimates and Solution Decomposition
.247
2
Finite Difference Methods
.259
2.1
Finite Difference Methods on Standard Meshes
.259
2.1.1
Exponential Boundary Layers
.259
2.1.2
Parabolic Boundary Layers
.266
2.2
Layer-Adapted Meshes
.268
2.2.1
Exponential Boundary Layers
.268
2.2.2
Parabolic Layers
.274
3
Finite Element Methods
.277
3.1
Inverse-Monotonicity-Preserving Methods Based on Finite
Volume Ideas
.278
3.2
Residual-Based Stabilizations
.302
3.2.1
Streamline Diffusion Finite Element Method
(SDFEM)
.302
3.2.2
Galerkin Least Squares Finite Element Method
(GLSFEM)
.327
3.2.3
Residual-Free Bubbles
.333
3.3
Adding Symmetric Stabilizing Terms
.338
3.3.1
Local Projection Stabilization
.338
3.3.2
Continuous Interior Penalty Stabilization
.352
3.4
The Discontinuous Galerkin Finite Element Method
.363
3.4.1
The Primal Formulation for a Reaction-Diffusion
Problem
.363
3.4.2
A First-Order Hyperbolic Problem
.368
3.4.3
dGFEM Error Analysis for Convection-Diffusion
Problems
.371
3.5
Uniformly Convergent Methods
.376
3.5.1
Operator-Fitted Methods
.377
3.5.2
Layer-Adapted Meshes
.381
3.6
Adaptive Methods
.407
3.6.1
Adaptive Finite Element Methods for Non-Singularly
Perturbed Elliptic Problems: an Introduction
.407
X
Contents
3.6.2 Robust
and Semi-Robust Residual Type Error
Estimators
.414
3.6.3
A Variant of the DWR Method for Streamline
Diffusion
.421
4
Time-Dependent Problems
.427
4.1
Analytical Behaviour of Solutions
.428
4.2
Finite Difference Methods
.429
4.3
Finite Element Methods
.434
Part IV The Incompressible Navier-Stokes Equations
1
Existence and Uniqueness Results
.449
2
Upwind Finite Element Method
.453
3
Higher-Order Methods of Streamline Diffusion Type
.465
3.1
The
Oseen
Problem
.466
3.2
The Navier-Stokes Problem
.476
4
Local Projection Stabilization for Equal-Order
Interpolation
.485
4.1
Local Projection Stabilization in an Abstract Setting
.486
4.2
Convergence Analysis
.488
4.2.1
The Special
Interpolant
.488
4.2.2
Stability
.489
4.2.3
Consistency Error
.491
4.2.4
A priori Error Estimate
.492
4.3
Local Projection onto Coarse-Mesh Spaces
.498
4.3.1
Simplices
.498
4.3.2
Quadrilaterals and Hexahedra
.499
4.4
Schemes Based on Enrichment of Approximation Spaces
.501
4.4.1
Simplices
.502
4.4.2
Quadrilaterals and Hexahedra
.502
4.5
Relationship to Subgrid Modelling
.504
4.5.1
Two-Level Approach with Piecewise Linear Elements
. 505
4.5.2
Enriched Piecewise Linear Elements
.507
4.5.3
Spectral Equivalence of the Stabilizing Terms on
Simplices
.508
5
Local Projection Method for Inf-Sup Stable Elements
.511
5.1
Discretization by Inf-Sup Stable Elements
.512
5.2
Stability and Consistency
.514
5.3
Convergence
.516
5.3.1
Methods of Order
r
in the Case
σ
> 0.517
5.3.2
Methods of Order
r
in the Case
σ
> 0.522
5.3.3
Methods of Order
r
+ 1/2.526
Contents
XI
6
Mass Conservation for Coupled Flow-Transport
Problems
.529
6.1
A Model Problem
.529
6.2
Continuous and Discrete Mass Conservation
.530
6.3
Approximated Incompressible Flows
.532
6.4
Mass-Conservative Methods
.534
6.4.1
Higher-Order Flow Approximation
.534
6.4.2
Post-Processing of the Discrete Velocity
.536
6.4.3
Scott-Vogelius Elements
.542
7
Adaptive Error Control
.545
References
.551
Index
.599 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Roos, Hans-Görg 1949- Stynes, Martin 1951- Tobiska, Lutz 1950- |
| author_GND | (DE-588)108923479 (DE-588)114088942 (DE-588)109576454 |
| author_facet | Roos, Hans-Görg 1949- Stynes, Martin 1951- Tobiska, Lutz 1950- |
| author_role | aut aut aut |
| author_sort | Roos, Hans-Görg 1949- |
| author_variant | h g r hgr m s ms l t lt |
| building | Verbundindex |
| bvnumber | BV035089815 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
| callnumber-search | QA377 |
| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 500 SK 920 |
| classification_tum | MAT 671f MAT 657f MAT 665f |
| ctrlnum | (OCoLC)222164146 (DE-599)BSZ285866427 |
| dewey-full | 518.63 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.63 |
| dewey-search | 518.63 |
| dewey-sort | 3518.63 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035089815 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:10:11Z |
| indexdate | 2024-07-09T21:21:57Z |
| institution | BVB |
| isbn | 9783540344667 9783540344674 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016757954 |
| oclc_num | 222164146 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-29T DE-11 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-29T DE-11 DE-83 |
| physical | XIV, 604 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spelling | Roos, Hans-Görg 1949- Verfasser (DE-588)108923479 aut Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems Hans-Görg Roos ; Martin Stynes ; Lutz Tobiska 2. ed. Berlin [u.a.] Springer 2008 XIV, 604 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 24 Perturbations singulières (Mathématiques) Équations différentielles - Solutions numériques Differential equations Numerical solutions Singular perturbations (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Singuläre Störung (DE-588)4055100-3 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Stynes, Martin 1951- Verfasser (DE-588)114088942 aut Tobiska, Lutz 1950- Verfasser (DE-588)109576454 aut 1. Auflage Numerical methods for singularly perturbed differential equations (DE-604)BV010616603 Springer series in computational mathematics 24 (DE-604)BV000012004 24 text/html http://swbplus.bsz-bw.de/bsz285866427kap.htm Kapitel 2 text/html http://swbplus.bsz-bw.de/bsz285866427kap-1.htm Kapitel 3 text/html http://swbplus.bsz-bw.de/bsz285866427inh.htm Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016757954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roos, Hans-Görg 1949- Stynes, Martin 1951- Tobiska, Lutz 1950- Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems Springer series in computational mathematics Perturbations singulières (Mathématiques) Équations différentielles - Solutions numériques Differential equations Numerical solutions Singular perturbations (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4055100-3 (DE-588)4012249-9 (DE-588)4128130-5 |
| title | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems |
| title_auth | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems |
| title_exact_search | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems |
| title_exact_search_txtP | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems |
| title_full | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems Hans-Görg Roos ; Martin Stynes ; Lutz Tobiska |
| title_fullStr | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems Hans-Görg Roos ; Martin Stynes ; Lutz Tobiska |
| title_full_unstemmed | Robust numerical methods for singularly perturbed differential equations convection-diffusion-reaction and flow problems Hans-Görg Roos ; Martin Stynes ; Lutz Tobiska |
| title_old | Numerical methods for singularly perturbed differential equations |
| title_short | Robust numerical methods for singularly perturbed differential equations |
| title_sort | robust numerical methods for singularly perturbed differential equations convection diffusion reaction and flow problems |
| title_sub | convection-diffusion-reaction and flow problems |
| topic | Perturbations singulières (Mathématiques) Équations différentielles - Solutions numériques Differential equations Numerical solutions Singular perturbations (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Perturbations singulières (Mathématiques) Équations différentielles - Solutions numériques Differential equations Numerical solutions Singular perturbations (Mathematics) Singuläre Störung Differentialgleichung Numerisches Verfahren |
| url | http://swbplus.bsz-bw.de/bsz285866427kap.htm http://swbplus.bsz-bw.de/bsz285866427kap-1.htm http://swbplus.bsz-bw.de/bsz285866427inh.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016757954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012004 |
| work_keys_str_mv | AT rooshansgorg robustnumericalmethodsforsingularlyperturbeddifferentialequationsconvectiondiffusionreactionandflowproblems AT stynesmartin robustnumericalmethodsforsingularlyperturbeddifferentialequationsconvectiondiffusionreactionandflowproblems AT tobiskalutz robustnumericalmethodsforsingularlyperturbeddifferentialequationsconvectiondiffusionreactionandflowproblems |
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